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# Design of Energy Harvesting based Hardware for IoT Applications

SatyaJaswanth Badri<EMAIL_ADDRESS>,  Mukesh Saini
<EMAIL_ADDRESS>and  Neeraj Goel<EMAIL_ADDRESS>Indian Institute of
Technology RoparS.Ramanujan Block, IIT Ropar Main CampusRoparPunjab,
India140001

###### Abstract.

Internet of Things (IoT) devices are rapidly expanding in many areas,
including deep mines, space, industrial environments, and health monitoring
systems. Most of the sensors and actuators are battery-powered, and these
batteries have a finite lifespan. Maintaining and replacing these many
batteries increases the maintenance cost of IoT systems and causes massive
environmental damage. Energy-harvesting devices (EHDs) are the alternative and
promising solution for these battery-operated IoT devices. These EHDs collect
energy from the environment and use it for daily computations, like collecting
and processing data from the sensors and actuators. Using EHDs in IoT reduces
overall maintenance costs and makes the IoT system energy-sufficient. However,
energy availability from these EHDs is unpredictable, resulting in frequent
power failures.

Most of these devices use volatile memories as storage elements, implying that
all collected data and decisions made by the IoT devices are lost during
frequent power failures, resulting in two possible overheads. First, the IoT
device must execute the application from the beginning whenever power comes
back. Second, IoT devices may make wrong decisions by considering incomplete
data, i.e., data-inconsistency issues. To address these two challenges, a
computing model is required that backs up the collected data during power
failures and restores it for later computations; this type of computing is
defined as intermittent computing. However, this computing model doesn’t work
with conventional processors or memories. Non-volatile memory and processors
are required to design a battery-less IoT device that supports intermittent
computing.

Energy-Harvesting, Data-Inconsistency, Intermittent Computing, Internet-of-
Things, and Non-Volatile Memory.

##  1\. Introduction

The Internet of Things (IoT) created many fascinating applications allowing
users to interact with numerous sensors and actuators. In many areas, such as
deep mines, health monitoring systems, industrial applications, and many other
fields, IoT helps to perform tasks that humans cannot do. For example, IoT
devices were used in the healthcare community to monitor glucose, heart rate,
and stress levels (Nguyen et al., 2017; Ghosh et al., 2020). Recent
advancements show that IoT devices assist in robotic surgeries and effectively
keep pacemakers near the patient’s heart (Yeole and Kalbande, 2016).

According to a study, billions of these sensors and actuators will be used in
real-time IoT environments by the end of 2050 (Golpîra et al., 2021). Most of
these IoT devices were powered by standard or rechargeable batteries, which
have a limited lifespan (Hu et al., 2020). Monitoring or replacing these many
batteries increases maintenance costs. Disposing of these many battery-powered
IoT devices harms the environment and reduces the device’s lifespan.

The alternative and promising technology that assists in replacing battery
technology is Energy-Harvesting devices (EHDs). These EHDs collect energy from
our surroundings (Chong et al., 2019; Ku et al., 2015), such as solar, piezo-
electric, wind, motion, breathing, etc. Solar voltaic cells, for example,
extract energy from the sun (Ku et al., 2015). Using these EHDs in an IoT
environment extends the life of the IoT devices. At the same time, the cost of
maintaining or charging these voltaic cells is significantly lower and more
cost-effective. Figure 1 shows the various energy-harvesting sources that are
available in our surroundings.

Figure 1. Different Energy Harvesting Resources Available in the Surroundings

These EHDs collect energy from their surroundings and store it in a capacitor,
where the stored energy is used by IoT devices to perform necessary
computations. Incorporating EHDs and a capacitor with the IoT devices makes
them battery-free devices (Mamen and Supatti, 2017). However, the energy
available from these EHDs is unstable, which may result in frequent power
failures. During power failures, the execution of these IoT applications may
become irregular, resulting in inconsistent output. As a result, a computing
model is required that enables IoT devices to backup and restore all the
computed results that are executed during these frequent power failures. This
computing model is known as intermittent computing (Lucia et al., 2017a;
Surbatovich et al., 2020; Hester and Sorber, 2017). This chapter discusses the
challenges associated with these devices and the hardware required for these
battery-free IoT devices that use harvested energy for executing the IoT
applications.

##  2\. Energy Harvesting in IoT devices & Environment

This section discusses the available energy sources in our surroundings and
how these EHDs benefit IoT devices and the environment. As shown in Figure 1,
there are four to five energy sources that are available in our surroundings,
including solar energy from the sun, mechanical energy from a nearby windmill,
RF energy from a Wi-Fi router, kinetic(mechanical) energy from water flow,
vibration(mechanical) energy from the road, and thermal energy from the heat
produced by the human body and the car. Human breathing and body movements can
also generate a small amount of energy.

Deploying EHDs for each energy source may accumulate a good amount of energy,
which can be helpful in executing IoT applications. EHDs such as solar voltaic
cells and PV panels harvest solar energy, which extracts energy in the range
of $15-100mW/cm^{2}$. The primary benefit of solar energy is its consistent
behavior; during the day, it harvests a large amount of energy from its
surroundings. The only drawbacks are its unpredictable behavior and deployment
constraints. EHDs like anemometers are used to harvest wind energy, which
extracts approximately $1200mWh/day$. The main advantage of wind energy is its
ease of deployment, and it can use in open areas. The only disadvantage for
these EHDs is maintenance costs.

EHDs, similar to piezoelectric materials, collect energy from human movements,
footfalls, and car vibrations on the road, extracting approximately $2.1-5W$
for human finger movements/footfalls and $200\mu W/cm^{2}$ for human motion.
Piezoelectric materials are fully controllable and produce energy based on our
needs. However, piezoelectric materials extract the least amount of energy.
EHD, like a ratchet flywheel, collects energy from human breathing, extracting
$0.42W$ of energy approximately. This energy-harvesting source is advantageous
because it is always available in our surroundings but produces little energy.

For extracting thermal energy (body heat, car engine heat), EHDs, such as
thermo-couple batteries, collect approximately $50mW/cm^{2}$. The main
advantage of these EHDs is that they are more reliable, require less
maintenance, and last longer. However, the energy conversion is very low and
insufficient for an IoT environment without additional support. EHDs such as
rectennas extract RF energy, which collects about $1W/cm^{2}$. The main
advantage of these EHDs is their mobility and high energy density. However,
these EHDs produce radioactivity, which may be more dangerous to people
nearby.

###  2.1. Internals of Energy-Harvesting-based IoT devices

Many of the EHDs are unpredictable and uncontrollable. Using energy-harvesting
resources in an IoT environment needs a proper energy management scheme.
Figure 2 shows the three main components of an energy-harvesting system (Ku et
al., 2015; Sanislav et al., 2021; Garg and Garg, 2017; Ma et al., 2017; Sahoo,
2016).

  1. (1)

Energy-Harvesting Resources: Resources that gather energy from their
surroundings.

  2. (2)

Energy-Monitoring System: Once the energy is extracted, a storage mechanism is
required to store and manage it.

  3. (3)

IoT devices & Environment: Effective utilization of stored energy is needed
for these IoT devices & the environment.

Figure 2. An Overview of Energy-Harvesting-based Architecture for IoT
Environment

After gathering energy from the environment, efficient mechanisms for storing
the collected energy are required. Rechargeable batteries, supercapacitors,
and thin-film batteries, among others, store enough energy within these
materials. Supercapacitors/thin-film batteries experience significant energy
leakage during charging and discharging cycles. As a result, management
techniques are also required to efficiently use accumulated energy by
allocating sufficient energy to IoT sensors and actuators based on their
needs. An efficient scheme or technique is required to monitor these leaks and
implement a near-zero leakage policy. Figure 2 shows an overview of the
energy-harvesting architecture used in the IoT environment.

The energy-monitoring system distributes energy to all IoT devices deployed in
the field. The majority of IoT devices and environments are composed of three
subsystems:

  1. (1)

The data collection unit contains many sensors and actuators that collect data
based on the IoT application.

  2. (2)

To store the computed results, a processing unit with memory and processors is
required to make the correct decision based on the data collected.

  3. (3)

Once a decision is made in a specific situation, the final decision must be
communicated to the other IoT device or end user via the communication unit.

###  2.2. Challenges associated with these energy-harvesting-based IoT devices

This section discusses the challenges associated with the energy-harvesting-
based IoT architecture shown in Figure 2.

  * •

Challenge 1: Energy availability is unpredictable and irregular. These EHDs
have no control over when and how much energy they collect.

  * •

Challenge 2: In the IoT environment, Issue-1 causes frequent power failures.
Because of these power failures, the execution model of the IoT application
becomes irregular.

  * •

Challenge 3: Figure 2 shows how supercapacitors are used as energy storage
mechanisms in an energy monitoring system. Once capacitors are connected to
IoT devices, the size of the capacitors is fixed, as is the amount of energy
stored in these capacitors. As a result, this constant amount of energy should
be used efficiently for IoT computations.

  * •

Challenge 4: There will be energy leakage from these capacitors/batteries and
an effective method is needed to monitor these energy leakage issues.

  * •

Challenge 5: Traditional processors and memory storage models are volatile in
today’s world. In these energy-harvesting-based IoT architectures, data
collected by IoT sensors and computation results may be lost during power
failures. When power is restored, the IoT application must start over,
consuming more energy by repeating the same procedures.

This chapter contributes to the discussion of the major problems related to
the energy-harvesting-based IoT architecture. This chapter also discusses
potential hardware for addressing the challenges listed above.

##  3\. Intermittent Computing

When there is enough harvested energy in a capacitor and the energy harvester
directly provides enough energy, the IoT application is run as usual, using
the energy directly from the harvester source. When the harvester does not
provide energy directly from the source, the IoT device must rely on energy
from the capacitor to perform essential tasks. Figure 3 shows enough solar
energy during the day for the IoT device to run the application without
intervention around 01:00 PM. The IoT device must use the capacitor’s energy
to complete important tasks before turning off in the evening, around 05:00
PM.

Figure 3. An Overview of Intermittent Computing for Solar-based Harvesting
Systems

Because energy is not always available to harvest, execution in such devices
is intermittent, resulting in power failures in the IoT environment (Lucia et
al., 2017a; Surbatovich et al., 2020; Hester and Sorber, 2017). Even when
energy is readily available, it takes time to accumulate enough energy to
perform valuable work. Incorporating new memory technologies and additional
procedures into the execution and memory model of a conventional processor is
required to design an intermittently aware design.

###  3.1. Memory Model for Intermittently Powered Devices

The hardware of an intermittently functioning device may include general-
purpose computing units such as a CPU or a microcontroller unit (MCU), a group
of sensors, and one or more radios to communicate with the sensor array.
Almost all of these devices use a volatile memory model. Figure 4 (a) shows
the conventional memory hierarchy, which includes the register file, caches,
main memory, and secondary storage. All other memories are volatile except for
secondary storage and can hold data only whenever power is available. As
illustrated in Figure 3, the IoT device will shut down when no energy is
available from the harvester source, i.e., at night (after 7:00 PM); during
this time, data stored in registers, caches, and main memory is lost.

Figure 4. Differences between Conventional and Non-Volatile Memory Models

There are two alternatives to keep the volatile contents safe. One approach is
to save all computed results and decisions made during the execution phase to
secondary storage before the MCU enters the power OFF state. The second
approach is to restart the IoT application whenever the energy harvester
provides enough energy to the MCU. Both alternatives are inefficient because
backup/recovery to/from secondary storage and re-executing the same
application take more time and energy. As a result, it is necessary to have a
memory model that can store the memory contents when the energy source is
unavailable.

Non-volatile memory (NVM) is a relatively new memory technology that can
retain the system state while consuming no power. NVM technologies are being
developed to overcome the drawbacks of volatile memory technologies. Flash,
spin transfer torque RAM (STT-RAM), phase-change memory (PCM), resistive RAM
(ReRAM), and ferroelectric RAM (FRAM) are examples of emerging NVM
technologies. Because of their exhibited physical properties, NVMs have the
potential to consume very little power while providing significantly greater
density than conventional memory technologies. A standard SRAM cell, for
example, has a size of $125-200F^{2}$, and a PCM and Flash cell have sizes of
$4-12F^{2}$ and $4-6F^{2}$, accordingly, where F refers to the lowest
lithographic dimensions that range in a specific technology node. Because of
their advantages, NVMs have become more common in products. Flash memory, for
example, is used as a cache in Intel TurboMemory.

These NVMs, however, have some limitations. NVMs, for example, have a higher
latency and consume more energy than volatile memory technology. Write
endurance is the property that determines how many writes a memory block can
withstand before it becomes ineffective. NVMs have significantly lower write
endurance than traditional memory technologies. Table 1 provides detailed
comparisons of various properties with various memory technologies. Access
granularity is defined as the minimum size of data read/written in each
access. Furthermore, they can store data for many years without requiring
standby power under regular circumstances. As shown in Table 1, the common
insight from all NVM technologies is that write latency/energy is greater than
read latency/energy (Mittal and Vetter, 2015; Boukhobza et al., 2017a; Ahmed
et al., 2021; Umesh and Mittal, 2021; Boukhobza et al., 2017b).

Table 1. Comparisons between different NVM Technologies for different Features

Property | SRAM | DRAM | HDD | SLC Flash | PCM | STT-RAM | ReRAM | FRAM
---|---|---|---|---|---|---|---|---
Cell Size ($F^{2}$) | $120-200$ | $6-12$ | NA | $4-6$ | $4-12$ | $6-50$ | $4-10$ | $12-15$
Read Latency |  $\sim$1 ns |  $\sim$110 ns | 5 ms | $25\mu s$ | 50 ns | ¡10 ns | ¡10 ns | 50 ns
Write Latency |  $\sim$1 ns |  $\sim$110 ns | 5 ms | $500\mu s$ | 500 ns | 10 ns | ¡10 ns | 50 ns
| Write Energy
---
(J/bit)
$\sim$ $10^{-15}$ |  $\sim$ $10^{-14}$ |  $\sim$ $10^{-14}$ |  $\sim$ $10^{-9}$ |  $\sim$ $10^{-11}$ |  $\sim$ $10^{-13}$ |  $\sim$ $10^{-13}$ |  $\sim$ $10^{-12}$
Leakage Power | High | Medium | Medium | Low | Low | Low | Low | Low
Erase Latency | NA | NA | NA | 2 ms | NA | NA | NA | NA
| Access Granularity
---
(B)
64 | 64 | 512 | 4K | 64 | 64 | 64 | 64
Endurance | ¿ $10^{16}$ | ¿ $10^{16}$ | ¿ $10^{15}$ | $10^{4}-10^{5}$ | $10^{8}-10^{15}$ | ¿$10^{15}$ | $10^{8}-10^{12}$ | $10^{10}-10^{12}$
Standby Power | $0.6-1.2W$ | Refresh Power | $1-2W$ | 0 | 0 | 0 | $0$ | $0$

In terms of characteristic features, STT-RAM outperforms all other NVM
technologies. Table 1 shows that STT-RAM outperforms other NVMs in terms of
write endurance, latency, and energy consumption. As a result, STT-RAM is a
promising candidate for cache, main memory, and scratch-pad memory. However,
because STT-RAM is more expensive than other NVMs, it is unsuitable for use at
the main memory level. PCM is the next better NVM technology after STT-RAM
because its size and write endurance are better than other NVMs. As a result,
PCM is a promising candidate for use in cache and main memory. However,
because STT-RAM has a longer lifespan than PCM, it is unsuitable for use at
the cache level. PCM is the better candidate for main memory. ReRAM and FRAM
share some characteristics; both were promising candidates for main memory.
ReRAM, on the other hand, has lower latency and energy consumption than FRAM.
For example, the MSP430FR6989 is a recent TI-based microcontroller with 2KB
SRAM and 128KB FRAM at the main memory level.

Incorporating NVMs at each level preserves the data in these IoT devices from
frequent power failures, switching the traditional processor into a non-
volatile processor. (NVP). Figure 4 (b) shows the memory hierarchy of non-
volatile flip-flops, non-volatile caches (STT-RAM/PCM), and non-volatile main
memory (PCM, ReRAM, and FRAM). Thus, replacing the non-volatile memory model
with volatile memory helps in intermittent computing and reduces the time and
energy required to backup/retrieve volatile contents.

####  3.1.1. Designing NVM-based Processor for Intermittently Powered IoT
Devices

A non-volatile processor (NVP) is designed by replacing volatile memory with
NVM at each level. Figure 5 shows two distinct architectures that demonstrate
the differences between pure NVM architecture and hybrid NVM architecture.
There is a pure NVM technology at each level in architecture-1, particularly
STT-RAM at both the L1 and last-level cache (LLC) levels and PCM at the main
memory level. In architecture-2, hybrid NVM technology is used at each level,
with SRAM+STT-RAM at the L1 and LLC levels and SRAM+PCM at the main memory
level (Xie et al., 2018; Instruments, 2018; Badri et al., 2023a; Jayakumar et
al., 2017; Badri et al., 2023b).

Figure 5. (a) Pure-NVM based architecture, STT-RAM at cache levels & PCM at
main memory level and (b) Hybrid-NVM based architecture, SRAM+STT-RAM at cache
levels & SRAM+PCM at main memory level

The main advantage of hybrid architecture over pure NVM architecture is that
it takes advantage of both SRAM and NVM, i.e., performance benefits from SRAM
and non-volatility and density benefits from NVM. Figure 5 (b) shows a design
that allows you to experiment with various combinations. As needed, the
designer must select hybrid NVM and pure NVM architectures. The main
disadvantage of using hybrid NVM over pure NVM architecture is that the
volatile contents in the hybrid architecture must be stored in NVM during
frequent power failures, which increases backup time and energy.

###  3.2. Execution Model for Intermittently Powered Devices

Regardless of several significant differences between the intermittent
execution model and the conventional embedded execution model, designers of
today’s intermittently powered devices use a standard, C-like embedded
computing abstraction. The application on an intermittently powered device
runs until the device’s energy has been drained. When the application’s energy
is restored, it resumes the execution from a specific point in its execution
history, such as the start of the main() function or a safe point. The primary
distinction between conventional and intermittent execution models is that a
normally executing program is expected to run until it is completed. In
contrast, an intermittent execution model must complete the program execution
despite multiple power interruptions. Various system components, such as
languages, application run time behavior, and program semantics, must be
modified to create an intermittence-aware design.

Among all of these changes, we highlighted three significant changes required
in the application execution flow for the intermittence-aware design.

Checkpoint(): When a checkpoint procedure is detected, all volatile contents
are copied to NVMs in order to preserve the system state. The existing
literature in this area focuses on when and where to place a checkpoint.
Recent research proposes two methods for determining when to perform this
checkpoint procedure.

  1. (1)

To monitor the energy source and capacitor, specially designed hardware is
required. When it falls below a certain threshold, the system sends an
interrupt, which stops the application and starts the backup() procedure.
Thus, checkpoints can occur at any time.

  2. (2)

Instead of maintaining hardware to monitor the energy requirements, existing
solutions track changes in the application state. There are solutions that
determine the variation at checkpoint time, either through hash comparisons or
by comparing main memory word-by-word with the most recent checkpoint data,
which is already in NVM. When there are many changes to initiate a backup()
procedure, the system issues an interrupt.

Backup(): Whenever a backup() procedure is initiated, it copies the volatile
contents to NVM, which means that it reads the contents from volatile memory
technology and writes them to NVM technology.

Restore(): Whenever a restore() procedure is initiated, it copies the backed-
up contents from NVM to volatile memory, which means it reads the contents
from NVM technology and writes them to volatile memory technology.

Adding additional procedures such as checkpoint(), backup(), and restore() to
the conventional execution supports intermittent computing, which also
completes Figure 3. However, these additional procedures may incur additional
costs. To reduce additional overheads in the intermittent execution model,
efficient checkpointing, backup, and rollback policies are required. Both the
execution and memory models support intermittently powered devices and
computing for these devices.

###  3.3. Challenges associated with these Intermittently Powered IoT devices

Intermittent computing introduces a number of challenges. These challenges
demonstrate how the system becomes inconsistent and fails to progress,
assisting an individual in developing an efficient intermittent-aware design
by dealing with these challenges properly.

####  3.3.1. Application Progress

If the application’s system state is not backed up completely across all power
failures, the application will re-execute from the beginning, i.e., from the
main() function (Lucia et al., 2017b, a; Surbatovich et al., 2020; Hester and
Sorber, 2017). Figure 6 (b) shows how the execution progress is affected by
frequent power failures. In Figure 6 (a), there is a backup() after the first
couple of instructions, and a power failure occurs after processing(result).
When power is restored, execution begins with sensing() rather than main(),
saving energy and time. However, when a power failure occurs again after
processing (result), the application enters an infinite loop, as illustrated
in Figure 6 (b). It never advances the execution of that instruction, and as a
result, the application never completes its execution and returns no results.

Figure 6. A detailed Example of Irregular Execution Progress during
Intermittent Power Supply (a) Application-1 without any Power failures, (b)
Execution of Application-1 during frequent Power failures, and (c) Execution
of Application-1 during frequent Power failures using the checkpointing
technique.

Specific checkpointing techniques must be incorporated into the application in
order to make consistent progress. Figure 6 (c) illustrates how inserting a
checkpoint after each instruction improves execution progress over the
previous approach (Figure 6 (b)). The programmer must ensure that each
checkpoint consumes one cycle of capacitor energy and that the distance
between checkpoints is acceptable to charge the capacitor sufficiently.

####  3.3.2. Memory Consistency

Most intermittently powered MCUs can have a mix of volatile and NVMs; the
MSP430FR6989, for example, has SRAM and FRAM. A naive design of volatile
memory and NVMs could lead to inconsistency in both memories (Lucia et al.,
2017b, a; Surbatovich et al., 2020; Hester and Sorber, 2017). Figure 7 shows
the application performing two tasks: incrementing an NVM variable, saving
variable data into an array1, and adding array elements, saving the final
value in the variable, where all array elements and results are stored in NVM.

Figure 7. A detailed Example of Memory Inconsistency behavior during
Intermittent Power Supply (a) Application-2 without any Power failures and (b)
Outputs after Executing Application-2 during frequent Power failures.

Assume there is a power failure between the increment operation and saving the
data into the array. In that case, the application’s entire system state is
lost, but not the data stored in the NVM, such as “D,” “arr1[],” and “result,”
as shown in Figure 7. When power is restored, the application begins again,
unaware of the fact that the data in NVM has already been
computed/incremented. As a result, in execution-2, the application increments
the variable “D” once more and computes the variable “result” using the
incorrectly stored array values, as illustrated in Figure 7 (b). During
frequent power failures, these memory inconsistencies increase, as illustrated
in Figure 7 (b). If the run-time system permits certain parts of the program
to be re-executed, it must also monitor and recover memory addresses that
could cause inconsistencies.

####  3.3.3. Preserving Program Semantics

Even if an application has well-suited checkpoints and a system that maintains
a consistent state between NVM and volatile memory, it may perform differently
than the designer expected. When the capacitor discharges and a power failure
occurs, the energy harvesting device is turned off for a defined period of
time, and all peripherals and their system states are cleared. When compared
to continuously powered devices, this behavior may violate the designer’s
assumptions about the atomicity of operations and the timeliness of data.

  1. (1)

Atomicity: Certain code regions must execute sequentially (with no checkpoints
in the middle), ensuring the application runs correctly. Before reading from a
sensor device, for example, the device driver checks that the sensing device
is turned on (enough energy is provided to the sensor) and that the bus is
ready to use because many sensor devices use this bus for communication with
other devices. Assume there is a checkpoint between these program assertions
and the sensor read function, and a power failure occurs. When power is
restored, the application returns to the previously saved checkpoint and
executes the sensor’s read function directly without performing the initial
checks. Designers should be able to specify which atomic regions must be
completed within a single energy peak.

  2. (2)

Timeliness: Some information loses value over time. Because the device may
remain turned off for a prolonged period of time if the power goes away,
placing checkpoints between the gathering and utilizing data restricts its
usefulness.

Consider an application that monitors a specific system’s temperature and
sends a radio signal alert indicating whether the temperature is appropriate
or exceeds a certain threshold. The application takes temperature readings but
terminates before they are completed. When the device is turned off, the
temperature changes dramatically. Whenever the application is restarted, the
device continues to process the stale data and incorrectly reports that the
system’s temperature readings are still acceptable. Programmers must be able
to communicate which events must occur in a timely fashion.

##  4\. Future Research Directions

Intermittent computing in energy-harvesting-based IoT devices is a new
research area that has the potential to design battery-free devices.

Programming Intermittent Devices: Despite the growing popularity of
intermittent devices, recent approaches to using them have several significant
drawbacks: (a) the developer’s effort in defining the tasks that IoT devices
must perform has been increased, (b) deciding the optimal size of each task,
(c) additional Overheads are due to run time exceptions and memory models, and
(d) inaccurate modeling of application-level characteristics (e.g., I/O
atomicity).

The limitations motivate more investigations to address the challenges
mentioned above by developing new programming models that reduce overheads and
the developer’s burden while maintaining developer control over atomicity.

Designing Distributed environment of intermittent devices: A communication
platform is required for distributed intermittent computing devices to
communicate with one another. The time between each communication consumes
less energy than the fixed communication span between these intermittent
computing devices compared to traditional communication platforms.
Synchronizing the collected data from these devices is an unresolved issue,
and monitoring the differences between synchronized and unsynchronized data
from these devices is also an open research problem.

The development of distributed systems that use intermittent devices allows
exceptional battery-free applications. The lack of programming tools &
environment, programming language specifications, memory & execution model
abstraction increases the complexity of designing an accurate, efficient,
distributed intermittent computing system. Recent measures have focused on
intermittent distributed shared memory models and simulator-based support.

Effective use of NVMs: Incorporating NVMs into intermittent systems consumes
more energy. So, when including NVM, efficient management and prediction
policies are required to reduce the overheads caused by NVMs and to use NVMs
efficiently. When using NVMs for hybrid caches/main memories, an optimal
placement policy that predicts which block should be placed in which memory
region is a crucial research objective. Recent research has centered on this
objective, proposing novel placement and prediction policies.

Efficient Checkpointing Policies: Checkpointing techniques are required to
keep the execution progress consistent. In an intermittent application
programmer inserts the checkpoints wherever it is needed. More checkpoints in
an application increase overheads due to unnecessary backup/restore to/from
NVMs and an increasing number of NVM accesses. As a result, the checkpointing
overhead consumes more energy than standard backup/restore procedures.
Determining when to checkpoint and which parts of an application to backup is
an unexplored research area. Reducing the number of unnecessary checkpoints
helps to reduce the time and energy required to backup/restore volatile
contents during a power failure.

##  5\. Conclusions

Battery-free devices are required for today’s IoT applications. Integrating
EHDs into an IoT environment introduces new challenges. In order to address
these challenges and gain support for intermittent computing, there is
necessary to change the conventional execution and memory model. The NVM
model, which replaces the traditional volatile memory model, assists in
support of intermittent computing. NVMs can store data even during a power
failure, making them useful as a backup/restore region for intermittent
computing. Many new NVM technologies have been proposed and are now on the
market. However, NVMs alone are insufficient for intermittent computing and
challenges due to unstable energy availability from harvesting resources. The
intermittent execution model includes different application procedures that
handle when and what to backup/restore to/from NVMs during frequent power
failures.

This chapter covers all aspects of intermittent computing for EHD-based IoT
devices. This chapter addresses all the modifications and hardware required to
replace existing models and energy-harvesting-based architectures in the IoT
environment. This chapter discusses how to turn battery-powered IoT devices
into batteryless IoT devices.

## Acknowledgement

This work is supported by the grant received from the Department of Science
and Technology (DST), Govt. of India, for the Technology Innovation Hub at the
IIT Ropar in the framework of the National Mission on Interdisciplinary Cyber-
Physical Systems.

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# On-chip topological transport of optical frequency combs in silicon-based
valley photonic crystals

Zhen Jiang1,2,# Hongwei Wang1,# Yuechen Yang1,2 Yang Shen1,2 Bo Ji1,2 Yanghe
Chen1,2 Yong Zhang,1 Lu Sun,1 Zheng Wang,1 Chun Jiang1<EMAIL_ADDRESS>Yikai Su1<EMAIL_ADDRESS>Guangqiang He1,2<EMAIL_ADDRESS>1State Key
Laboratory of Advanced Optical Communication Systems and Networks, Department
of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240,
China
2SJTU Pinghu Institute of Intelligent Optoelectronics, Department of
Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
#These authors contributed equally to this work.

Quantum optical combs, valley photonic crystal, dissipative Kerr soliton combs

††preprint: APS/1

The generation and control of optical frequency combs in integrated photonic
systems enables complex, high-controllable, and large-scale devices. In
parallel, harnessing topological physics in multipartite systems has allowed
them with compelling features such as robustness against fabrication
imperfections. Here we experimentally demonstrate on-chip topological
transport for optical frequency combs at telecommunication wavelengths, both
in classical and nonclassical domains. We access both the quantum frequency
combs and dissipative Kerr soliton combs with a micro-resonator. The quantum
frequency comb, that is, a coherent superposition of multiple frequency modes,
is proven to be a frequency-entangled qudit state. We also show that
dissipative Kerr soliton combs are highly coherent and mode-locked due to the
collective coherence or self-organization of solitons. Moreover, the valley
kink states allow both quantum frequency combs and dissipative Kerr soliton
combs with robustness against sharp bends. Our topologically protected optical
frequency combs could enable the inherent robustness in integrated complex
photonic systems.

##  I Introduction

Integrated optical frequency combs (OFCs) in classical and quantum domains are
undergoing a revolutionary development due to the advances in nanofabrication
techniques. OFCs characterized by phase-coherent, uniformly spaced narrow
laser lines can greatly extend the frequency domain channels, therefore, they
have a great potential to increase the number of effective dimensions of
photonic systems [1, 2, 3]. As a type of OFCs, quantum frequency combs (QFCs)
generated at the single-photon level are particularly important for quantum
information science due to their high-dimensional distributions in the
frequency and time domains [4, 5, 6]. QFCs have demonstrated high-dimensional
frequency entanglement [7, 8, 9], energy-time entanglement [10, 11, 12], and
time-bin multiphoton entanglement [13], which provide practical applications
in quantum communication [14] and quantum computing [15]. For classical
frequency combs, mode-locking approaches provide high stability for fully
coherent dissipative Kerr soliton (DKS) combs, which have been used in
ultrafast ranging [16, 17, 18, 19], optical communications [20], optical
spectroscopy [21, 22], frequency synthesis [23, 24], and optical computing
[25, 26]. However, the self-coherent frequency combs, especially QFCs, are
fragile due to decoherence and fidelity degradation in noisy environments [27,
28].

Meanwhile, topological photonics has paved the way for robust optical
transmission utilizing topological protection, which can be categorized into
quantum Hall effect [29, 30, 31], quantum spin Hall effect (QSH) [32, 33, 34,
35] and quantum valley Hall effect (QVH) [36, 37, 38, 39]. They have given
rise to new paradigms of optical functional devices characterized by
directional transmission and high interference immunity. Recently, significant
advances have been made in topological nonlinear and quantum photonics,
including topological nonlinear harmonic generation [40, 41], topological
nonlinear imaging [42], topological single-photon and biphoton states [43, 44,
45], topological quantum emitters [28], and topological quantum interference
[46, 47]. Topological quantum entanglement in coupled resonator arrays
emulating the Su–Schrieffer–Heeger (SSH) model has been experimentally
proposed [28]. However, the coupled resonator arrays have large chip sizes and
are inconvenient for optical modulation. The topological transport in
multiparty and high-dimensional entangled QFCs remains to be established. The
valley photonic crystal (VPC) waveguides have advantages in large bandwidth
and super-compact chip sizes. Hence they are convenient for optical
modulation, offering exciting possibilities for on-chip robust topological
transport of high-dimensional entangled QFCs.

Here we experimentally demonstrate on-chip topological transport for both QFCs
and DKS combs generated from the same silicon nitride ($\rm Si_{3}N_{4}$)
micro-resonator. A VPC-based waveguide supporting topologically protected kink
states is fabricated on a silicon-on-insulator (SOI) slab. Employing a $\rm
Si_{3}N_{4}$ micro-resonator with an approximate 100 GHz free spectral range
(FSR), we can access QFCs and DKS combs by pumping different powers. On the
one hand, we measure the coincidence-to-accidental ratio (CAR) and joint
spectral intensity (JSI) of QFCs after their transport to topological
interfaces. By calculating the Schmidt numbers of the QFC, we show that it
remains a two-photon entangled qudit state. This indicates that the entangled
biphootn state is robust against structural imperfections. On the other hand,
we also access DKS combs operating in single soliton, multiple solitons, and
soliton crystals, respectively. Although these DKS combs traverse the
topological interfaces, they still retain their distinctive DKS-like
characteristics. Topologically protected kink states effectively preserve the
integrated micro-combs, both QFCs and DKS combs, making them robust against
sharp bends and structural imperfections. Our findings show the potential for
achieving topologically unidirectional transport of high-dimensional entangled
states and phase-locked soliton states in VPC slabs. From an application
standpoint, this proposition could open new avenues for high-dimensional
information processing utilizing topology in both classical and quantum
optics.

##  II Design of VPCs

Our topological VPCs are fabricated based on a SOI wafer with a thickness of
the silicon layer 220 nm (see Methods). As shown in Fig.1a, the VPCs are
composed of a graphene-like lattice of triangular holes lattice with a lattice
constant $a_{0}=433$ nm. Two types of triangular stomata with different side
lengths form the honeycomb valley photonic structure, where the two side
lengths are characterized by $d_{1}$ and $d_{2}$, respectively.

Figure 1: Energy band diagram and transmittance of the topological edge state
based on VPCs. a The red dashed hexagon in the figure represents the unit cell
of the VPC slab with the lattice constant $a_{0}=433$ nm ($d_{1}=122$ nm and
$d_{2}=295$ nm). b Band diagram of the VPC slab with inversion symmetry (red-
dotted curves) compared with inversion symmetry breaking (black-diamond
curves). $\Gamma$, K and M denote the high-symmetry points in the first
Brillouin zone. c Edge dispersion of the edge state (blue-diamond curves). d
$H_{z}$ field distributions for the topological edge state based on VPCs along
the x direction. d,e Scanning electron microscope (SEM) images of the straight
and Z-shaped topological waveguides, respectively. f Measured transmission
spectra of the straight interface (orange curve) and Z-shaped interface (green
curve), respectively.

As shown by the red-dotted curve in Fig.1b, due to $C_{6}$ symmetry, a Dirac
point appears at approximately $\lambda=1566$ nm at the Brillouin zone corners
($\rm K$ and $\rm K^{\prime}$) where $d_{1}=d_{2}=216$ nm. The inversion
symmetry of the VPC can be broken by assigning mismatched wall-length
parameters ($d_{1}=122$ nm and $d_{2}=295$ nm), which opens a band gap as
illustrated by the black-dotted curve in Fig.1b. It is noted that the modes at
the $\rm K$ and $\rm K^{\prime}$ valleys exhibit opposite polarizations, which
are commonly referred to as left-handed circular polarization and right-handed
circular polarization, respectively. [36, 37] Then we define the VPCs as $\rm
VPC_{1}$ ($d_{1}=122$ nm and $d_{2}=295$ nm) and $\rm VPC_{2}$ ($d_{1}=295$ nm
and $d_{2}=122$ nm), respectively. They have the opposite valley Chern
numbers, i.e., $C_{v1}<0$ for $\rm VPC_{1}$ and $C_{v2}>0$ for $\rm VPC_{2}$
(for details, see Supplementary Section I). At the interface between $\rm
VPC_{1}$ and $\rm VPC_{2}$, the reversion of the two VPCs leads to the
reversion of the sign of the Berry curvature at the valleys, according to the
bulk-boundary correspondence, it may exhibit a pair of counter-propagating
valley kink states. As shown in Fig.1d, the edge state exists at the
topological interface between $\rm VPC_{1}$ and $\rm VPC_{2}$, the difference
between the valley indices at the K point across the interface is $\Delta
C_{{}_{edge1}}^{K}=C_{{}_{\nu 2}}-C_{{}_{\nu 1}}>0$ [36, 48], which determines
the propagation direction of the fringe state around each valley.

The dispersion of the edge state is shown in Fig.1c (blue curve). There exists
a pair of valley kink states with a topological bandgap of valley kink states
is approximately 25 THz (from 175 THz to 200 THz). Such a large bandwidth
allows the topological transport of OFCs with a bandwidth of approximately 200
nm at telecommunication wavelengths. This pair of valley kink states with
opposite group velocities are locked to valleys, which is referred to as
“valley-locked” chirality [34, 36]. Furthermore, to verify the robustness
against the sharp turns, we design two types of waveguides, that is, the
straight and Z-shaped topological waveguides. The SEM figures of two
topological waveguides are shown in Fig.1e,f, respectively. The in-and-out
coupling of topological waveguides is achieved using lensed fibers with an
overall measured insertion loss of 12 dB. The measured transmission spectra of
the light propagation along the interfaces of a 60-degree turn are similar to
those along a straight interface, which shows that the propagation of light
along the topological waveguide is topologically protected (Fig.1g). We can
observe a topological bandgap from 1490 nm to 1640 nm, where the transmission
(above 1640 nm) can not be measured due to the cutoff excitation wavelengths
of the pump laser. Besides, we also simulate the field profiles of valley kink
states at the frequency of 193 THz (around 1550 nm), which also reveals the
light confinement and robustness against shape corners (see Supplementary
Section II for details).

##  III Topological transport of QFCs

The concept of topological protection harnessed through valley-dependent edge
states, finds applicability in the transport of on-chip QFCs. We first perform
on-chip topological transport of QFCs with frequency entanglement. Our QFC is
generated in a $\rm Si_{3}N_{4}$ microring resonator with the high-quality
factor ($Q$-factor) of $1.68\times 10^{6}$ (see Supplementary Section III for
details).

To manipulate the broadband phase matching for spontaneous FWM, we carefully
design waveguide cross-section with weak and anomalous group-velocity
dispersion (GVD) [1]. As a result of the spontaneous FWM process, a two-photon
high-dimensional frequency-entangled state, also referred to as a biphoton
frequency comb (BFC), can be accessed [6]. For a QFC, an individual signal or
idler photon is a coherent superposition of multiple frequency bins. The high-
dimensional frequency entanglement of biphoton frequency combs will increase
the capability of quantum information processing [7, 13].

Our experimental setup for the topological transport of quantum frequency
combs is schematized in Fig.2a (see Methods). We pump the $\rm Si_{3}N_{4}$
micro-resonator to below-threshold pumping at approximately 1550 nm. The
spontaneous FWM process leads to a BFC, such a high-dimensional entangled
state can be written as [7]:

$|\Psi\rangle=\sum_{k=1}^{N}\alpha_{k}|k,k\rangle_{si},\mathrm{with}\sum|\alpha_{k}|^{2}=1,$
(1)

where $k$ is the mode number and the complex element $\alpha_{k}$ represents
the amplitude and phase of the signal–idler photon pair, the quantum state
$|k,k\rangle_{si}$ is given by

$|k,k\rangle_{si}=(\Omega-k\Delta\omega)|\omega_{p}+\Omega,\omega_{p}-\Omega\rangle_{si},$
(2)

in which $\Omega$ is the frequency deviation from the pump frequency
$\omega_{p}$, $\Delta\omega$ is the FSR of the resonator. $f(\Omega)$ is the
Lorentzian spectrum function. We can deduce that the quantum state
$|k,k\rangle_{si}$ embodies a superposition encompassing numerous
symmetrically arranged pairs of signal and idler frequencies around the pump
frequency.

After the rejection of the pump light with a filter, this QFC is coupled into
two VPC waveguides. Two tunable bandpass filters (TBPFs) are used to select
the signal and idler frequency modes, and send them to two InGaAs single
photon detectors (SPDs) for counting measurement. Figure 3a depicts the
measured single-photon spectrum of the original QFC. Also, the single-photon
spectrums of QFCs at the output ports of both straight and Z-shaped
topological waveguides are also depicted in Fig.3b, c. The wavelength
bandwidth of these frequency modes is around 0.8 nm, which corresponds to the
FSR of $\rm Si_{3}N_{4}$ micro-resonator (about 100 GHz). The single photon
spectrum is consistent with the operation bandwidth of valley kink states,
while the QFC within the bulk bands is rejected. Notably, thanks to the broad
bandwidth of topological waveguides, we can clearly observe QFCs ranging from
1510 to 1590 nm, corresponding to around 10 THz bandwidth. As a consequence of
energy conservation, the signal and idler photons are highly correlated in
frequency and time domains.

Figure 2: a Experimental setup for topological transport of OFCs. For the
generation of QFCs, the pump laser is actively tuned by proportional-integral-
differential (PID) controller, while the auxiliary laser is not used. For the
generation of DKSs, both two lasers are utilized to pump the resonator. EDFA,
erbium doped fiber amplifier; FPC, fiber polarization controller; CIRC,
optical circulator; OPM, programable optical power meter; FBG, fiber Bragg
grating; OSA, optical spectrum analyzer; ESA, electrical spectrum analyzer. b
Experimental setup for the spectrum of DKSs. c Characterization of correlation
properties and joint spectral intensity of QFCs. d Experimental setup for RF
beatnotes of the single soliton states and a CW reference laser. Figure 3:
Measured single-photon spectrum at the outputs of the a original micro-
resonator, b straight, and c Z-shaped topological waveguides, respectively.
The red, blue, and yellow marked regions denote the selected signal modes,
idler modes, and several modes eliminated by the FBG, respectively. Signal-
idler coincidence histograms for correlated photon pairs ($S_{7}I_{7}$) and
uncorrelated photon pairs ($S_{7}I_{8}$) at the outputs of the d original
micro-resonator, e straight and f Z-shaped topological waveguides,
respectively.

To confirm the quantum correlation of our QFCs, we record the relative arrival
time between correlated photon pairs ($S_{7}I_{7}$) and uncorrelated photon
pairs ($S_{7}I_{8}$) as coincidences. As illustrated in Fig.3d-f, the
coincidence peaks are only measured with wavelength-correlated cases, while
the absence of coincidence peaks between the photon pairs $S_{7}I_{8}$
indicates the absence of correlation between frequencies that are not matched.
Notably, any event for uncorrelated photon pairs is considered an accidental
count, which includes dark counts, background, and uncorrelated photon counts
[11]. We fit three coincidence peaks by Glauber second-order (cross)
correlation function $g_{si}(\Delta t)\propto exp[-\Delta t/\tau]$ [49], where
$\tau$ is the coherence time of the corrected photons. The fitted coherence
times of the photons in three cases are 2.90 ns, 2.69 ns, and 2.45 ns,
respectively, which are in agreement with the resonance linewidth ($~{}115$
MHz). In addition, we characterize the quantum correlation property of photon
pairs ($S_{7}I_{7}$) by the CAR with 9.7, 10.7, and 10.2, respectively. Note
that high on-chip power (6 mW) increases the accidental counts, and then,
leads to lower values of CAR.

Figure 4: Measured joint spectral intensity at the outputs of the a original
micro-resonator, b straight, and c Z-shaped topological waveguides,
respectively. The distributions of normalized Schmidt coefficients
$\lambda_{n}$ for the d original QFC, the QFCs after the transport of the f
straight and h Z-shaped topological waveguides, respectively. The entanglement
entropy $S_{k}$ for the e original QFC, the QFCs after the transport of the g
straight and i Z-shaped topological waveguides, respectively.

We also performed the calculation of the heralded efficiency $\eta_{h}$,
representing the probability of detecting an idler photon when the signal
photon is detected. Generally, the heralded efficiency can be given by
$\eta_{h}={cc}/{c_{signal}\eta_{det}}$ [50], where $cc$, $c_{signal}$ are
coincidence and signal count rate respectively, $\eta_{det}$ denotes the
detection efficiency of the SPD for idler mode (20$\%$). Based on the obtained
measurement, we derive a heralding efficiency of $\eta_{h}=6\%$, without
including losses of the experimental setup.

Furthermore, to evaluate spectro-temporal correlations across the photon-pair
spectrum, we conducted measurements of the JSI utilizing two TBPFs. Here we
consider time correlation measurement for mode-by-mode photon count covering 5
sideband pairs ($S_{4-8}I_{4-8}$). To mitigate the influence of accidental
counting events, we subtract the accidental coincidence counts. It is
important to emphasize that the JSI distribution outlines the probability
distribution across two dimensions for signal and idler photons [51]. As shown
in Fig.4a, photon pairs satisfying the energy conversion relation
($2\omega_{p}=\omega_{s}+\omega_{i}$) exhibit pronounced frequency
correlation. In general, the JSI may be given by
$|(\mathcal{A}(\omega_{s},\omega_{i})|^{2}=|A(\omega_{s},\omega_{i})|^{2}|\Phi(\omega_{s},\omega_{i})|^{2}$,
where $\Phi(\omega_{s},\omega_{i})$ is corresponding to the phase matching
properties and spatial characteristics of the pump beam. Hence, the JSI
$|(\mathcal{A}(\omega_{s},\omega_{i})|^{2}$ demonstrating spectral
correlations arises from the energy and momentum conservation [51].

To quantify the entanglement within quantum frequency combs, a valuable
approach known as Schmidt decomposition is employed to assess the separability
of the joint spectral amplitude (JSA), with a part of phase information
disregarded. The JSA can be approximated from the JSI as
$\mathcal{A}(\omega_{s},\omega_{i})\approx\sqrt{|(\mathcal{A}(\omega_{s},\omega_{i})|^{2}}$
[7]. It’s worth noting that the state $|\Psi\rangle$ is frequency entangled
when a probability distribution JSA cannot be decomposed into the function of
$\omega_{s}$ and $\omega_{i}$. Employing the Schmidt decomposition (see
Supplementary Section V), we can access the Schmidt numbers of our QFCs [52].
Figure 4d-i show the distributions of normalized Schmidt coefficients
$\lambda_{n}$ and entanglement entropy $S_{k}$. Note that the Schmit
coefficients $\lambda_{n}$ represent the possibility of obtaining the $n$th
quantum state, where the presence of nonzero Schmidt coefficients (greater
than 1) indicates the frequency entanglement characteristic of topologically
protected QFCs [53]. Additionally, the entanglement entropy
$S_{k}=-\sum\lambda_{n}\log_{2}\lambda_{n}$ can describe the degree of
entanglement. The entanglement entropy $S_{k}$ is quantified as 1.41, 0.94,
and 0.6, respectively. It serves as evidence of entanglement when $S_{k}>0$.

The Schmidt number is deducible from $K=(\sum\lambda_{n}^{2})^{-1}$, yielding
the specific values of 1.88, 1.42, and 1.2 for three cases. The small values
of these Schmidt numbers arise from undesired accidental counts within off-
diagonal components, primarily stemming from afterpulse detection and dark
counts of InGaAs SPDs. Notably, these phenomena tend to introduce undesired
noise. The Schmidt numbers could be readily enhanced by using superconducting
nanowire single photon detectors (SNSPDs), which can significantly reduce the
aforementioned issues. Assume the off-diagonal elements are entirely
eliminated within our measured JSI, a Schmidt number above 4.0 can be
attained. In a highly multi-dimensional space, the resulting Schmidt number
$K$ serves as an effective way for quantifying the high-dimensional frequency
entanglement. The Schmidt number $K$ effectively characterizes the minimum
count of pertinent orthogonal modes within a bipartite system. In the case of
a separable system, the JSA satisfies
$\mathcal{A}(\omega_{s},\omega_{i})=\psi_{n}(\omega_{s})\phi_{n}(\omega_{i})$,
thereby resulting in a Schmidt number $K=1$ [54]. For our QFC, the biphoton
entangled quantum state encompasses numerous frequency modes, thereby giving
rise to frequency entanglement [52]. The unambiguous observation of QFCs
serves as clear evidence supporting the achievement of topological transport
for high-dimensional quantum entangled states.

Alternatively, one can eliminate the single-photon purity linked to the
factorizability of two biphoton states from Schmidt decomposition. Purity is
indispensable for achieving high-visibility quantum interferences between
photons originating from the same source. Generally, the single-photon purity
can be given by $\text{Tr}(\hat{\rho}_{\text{s}}^{2})$, where
$\hat{\rho}_{\mathrm{s}}=\mathrm{Tr}_{\mathrm{i}}(|\Psi\rangle\langle\Psi|)$
is the density operator for the heralded single photon, and
$\mathrm{Tr}_{\mathrm{i}}$ denotes the partial trace over the idler mode. The
heralded single-photon purity $\text{Tr}(\hat{\rho}_{\text{s}}^{2})$ can be
given by $\text{Tr}(\hat{\rho}_{\text{s}}^{2})\overset{}{=}K^{-1}$ [51].
Consequently, the single-photon purity for our QFCs in three cases is
calculated as 0.53, 0.70, and 0.83, respectively.

##  IV Topological transport of DKS combs

We also perform on-chip topological transport of DKS combs, the experimental
procedure is depicted in Fig.2a. An integrated $\rm Si_{3}N_{4}$ micro-
resonator provides a reliable platform for manipulating temporary DKS combs at
the telecommunication wavelengths. Before our experimental scheme, we
numerically simulated the soliton generation described by Lugiato–Lefever
equation (LLE) (see Supplementary Section VI). For solitons generation, it is
crucial for the laser wavelength to precisely stabilize at the soliton steps.
However, limited by the frequency tunning accuracy or stability of pump
lasers, as well as thermal instability within the range of existing solitons,
it becomes a challenge for the generation of DKSs within micro-resonators
characterized by short thermal lifetimes [1]. Therefore, a dual-pump method is
utilized to produce DKS combs in the same micro-resonator (see Methods), where
an auxiliary laser is introduced to stabilize the intracavity energy, thereby
facilitating the extension of soliton steps. Except for the benefits of
thermal stability, the beating between the auxiliary and pump lasers would be
useful for facilitating the generation of soliton crystals [55].

Figure 5: Optical spectrum of the single soliton state at the outputs of a the
original micro-resonator, b straight, and c Z-shaped topological waveguides,
respectively. Optical spectrum of the multisoliton state at the outputs of d
the original micro-resonator, e straight, and f Z-shaped topological
waveguides, respectively. Optical spectrum of perfect soliton crystals at the
outputs of g the original micro-resonator, h straight, and i Z-shaped
topological waveguides, respectively.

With the scanning of the pump laser from ‘blue’ to ‘red’ laser-cavity, one can
clearly observe the comb evolution processes including Turing rolls, chaotic
states (breathing solitons), multisolitons, and single solitons, respectively
[56]. Generally, a sharp drop in the generated comb power signifies the arrive
of the bistable region, precisely revealing the appearance of solitons, which
is also commonly referred to as the ’soliton step’ [1].

The produced DKS combs are split by a 90:10 beam splitter (BS), where 10$\%$
of the resulting comb output is directed towards an OSA to assess the spectrum
of the original Kerr combs. Meanwhile, the remaining 90$\%$ of the output is
coupled into the topological waveguide following polarization control.
Subsequently, the output of the topological waveguide is directed to another
OSA, allowing for the monitoring of its spectral properties.

DKS states are readily accessed by stopping the laser at distinct steps. A
single soliton state and its transmission spectrum at the output ports of both
straight and Z-shaped topological waveguides are shown in Fig.5a-c. Note that
the frequency modes of the pump laser and FWM sidebands generated from the
auxiliary laser in the optical spectrum are removed. The associated optical
spectrum reveals line spacing matches the resonator FSR over a range of around
20 THz, and also exhibits smooth $\rm sech^{2}$-shaped spectral envelopes. The
single soliton spectrum has a 3-dB bandwidth of $\sim$29.3 nm corresponding to
a soliton pulse width of $\sim$87.5 fs. To further verify the coherence of
single soliton states, we beat one of the spectral lines of the comb with a CW
laser. The beat notes show distinct frequency lines with resolution bandwidths
(RBWs) of 100 kHz and signal-to-noise ratios of 30 dB (see Supplementary
Section VII), leading to outstanding low-noise characteristics.

Due to the inherently stochastic nature of intracavity dynamics, multisolitons
with a random soliton number $N$ could be assessed during the frequency-tuning
procedure [1]. The spectral envelopes of the multisoliton state emerge from
the interference between multiple solitons, and become more complicated as the
number of solitons increases [56]. In other words, the intracavity solution
for the multisoliton state can be expressed as a summation of distinct,
independent soliton solutions situated at various positions, as depicted in
Figure 5d-f. Strikingly, An adiabatic backward tuning method can successfully
reduce the soliton number, which makes it reliable to access the single
soliton state from the multisoliton state [1].

We also access perfect soliton crystals using the forward tuning pump at
relatively low pump powers (100 mW). Perfect soliton crystals, that is, a
collective self-organization result of the multiple solitons. The transmission
spectrum of original perfect soliton crystals is shown in Fig.5g, while the
spectra after the transport of both straight and Z-shaped topological
waveguides are shown in Fig.5h,i. The combs show several evenly distributed
supermodes separated by 13 FSRs, leading to a mode spacing of 1.24 THz. Also,
our perfect soliton crystals can be regarded as a single soliton with larger
FSR, which can be applied in the generation of ultra-high-repetition rate DKS
combs [53]. In the time domain, there are 13 DKSs in the resonator with a
time-independent pulse separation of $2\pi/13$, reaching the maximum allowed
number of solitons existing with the given pump. Since the comb power is
distributed in such 13 supermodes, the power of each supermode is enhanced by
$13^{2}$ times, and energy conversion efficiency by 13 times compared with the
single soliton state [56].

Due to the broad bandwidth of topological waveguides, we show the topological
transport of DKS combs with a range of around 20 THz, and all DKS combs can
smoothly pass through sharp bends without visible loss. Despite transport
along sharp turns, our DKSs retain their characteristics, including the
specific spectral envelopes and low-noise operation.

##  V Conclusion

In this work, we experimentally demonstrated on-chip topological transport for
optical frequency combs at telecommunication wavelengths. We show topological
valley kink states are robust against sharp turns in a VPC slab. We access
both the two-photon frequency-entangled QFC and mode-locking DKS combs with a
$\rm Si_{3}N_{4}$ micro-resonator. For our QFCs, a coherent superposition of
multiple frequency modes leads to a frequency-entangled qudit state. This
qudit state maintains its strong frequency correlation with the transport
along topological interfaces with sharp bends. In particular, the QFCs also
have the potential to be energy-time entanglement, which can be detected by
quantum interference in a Franson-type interferometer [11, 12]. Such
topologically protected QFCs provide robust, complex, high-controllable, and
large-scale quantum resources, which may scale up quantum communication, as
well as quantum information processing. In addition, we also demonstrate the
topological transport of mode-locked DKS combs in our design, revealing that
DKSs keep their perfect spectral phase and temporal pulse shape. The ultrahigh
stability and low-noise characteristics of topologically protected DKS combs
provide new applications in metrology and spectroscopy.

##  VI Methods

###  VI.1 Device fabrication

We fabricated the proposed topological device on an SOI wafer with a 220 nm
thick top silicon layer and 3 $\mu m$ thick buried silicon layer. The edge
coupler, silicon waveguide, and VPC structures were etched to a depth of 220
nm. Subsequently, we deposited a 1 $\mu m$ thick $\rm SiO_{2}$ cladding using
plasma-enhanced chemical vapor deposition (PECVD). Finally, the whole chip was
deeply etched and cut into several individual chips. The devices were
fabricated using electron beam lithography (Vistec EBPG 5200+) and an
inductively coupled plasma etching process (SPTS DRIE-I). For details on the
fabrication process of the structures presented in this study, see Refs. [57,
58].

###  VI.2 Experimental setup for QFCs generation

In this experiment, we use a compact CW laser (Pure Photonics) with a
wavelength of 1550.78 nm to pump the $\rm Si_{3}N_{4}$ micro-resonator and an
EDFA to amplify the pump. Two cascaded bandpass filters are used to suppress
the ASE noise produced by the EDFA. The measured power coupling into the
resonator is 6 mW. A TEC is applied to control the thermal instability of the
resonator with the injection of the pump. The output QFC is coupled into
topological waveguides after the polarization adjustment by a FPC. At the
output port, a 99:1 BS is connected, where 1$\%$ of the output power is
detected by a programable OPM (Joinwit) to monitor the pump power. This part
of the output pump monitored by an OPM is used to actively control the
wavelength of the CW laser by PID algorithm. The application of PID control
ensures a stable resonant state for long-time coincidence measurement. The
other 99$\%$ of output power is rejected by an FBG, and the remaining QFCs are
split by a 50:50 BS. The signal and idler modes are selected by two TBPFs (WL
Photonics) with a bandwidth of 0.11 nm, and detected by two InGaAs SPDs (Aurea
Technology). For the single photon spectrum measurement, the SPDs are set to
gated mode with 20$\%$ quantum efficiency and 10 $\rm\mu$s dead time. For the
JSI measurement, the SPDs are set to gated mode (20 MHz repetition rate) with
20$\%$ quantum efficiency and 10 $\rm\mu$s dead time and then sent to a time
analyzer to record coincidence events between signal and idler photons.

###  VI.3 Experimental setup for DKS combs generation

In this experiment, we use the dual-pump method to produce DKS combs by a
computer-controlled soliton generation system [59]. The pump laser is excited
by the same CW laser, and amplified to 0.4 W by an EDFA. The EDFA amplified
spontaneous emission (ASE) noise is suppressed by two cascaded bandpass
filters. An extra auxiliary laser with 1 W power is employed to stabilize the
intracavity energy for extending the steps of solitons. To reduce the crossed
interaction of the two pumps, they are changed to orthogonal modes by two
independent fiber FPCs. Then these two lasers are injected into the bus
waveguide in opposite directions, with two circulators separating the input
and residual pump light. Besides, a TEC is applied to control the thermal
instability of the micro-resonator. The output comb is split by a 99:1 BS,
with 1$\%$ of the output power detected by an OPM. The other 99$\%$ of output
power is separated by a 90:10 BS, with 10$\%$ of residual output sent to an
OSA to measure the spectrum of generated Kerr combs, while 90$\%$ of residual
output is coupled into the topological waveguide after the polarization
control. Then the output of the topological waveguide is sent to another OSA
to monitor its spectrum. For the computer-controlled soliton generation
system, the auxiliary laser is tuned at the resonance wavelength to produce
primary FWM sidebands. The pump laser is automatically tuned from the blue to
red side to assess the soliton states. in this process, the script will assess
the intracavity state by the measured output power. Once the soliton state is
accessed, the automation script gives the “stop” order for the pump laser (see
Supplementary Section IV). In this case, the soliton state will hold for
several hours.

###### Acknowledgements.

This work is supported by the Key-Area Research and Development Program of
Guangdong Province (2018B030325002), the National Natural Science Foundation
of China (62075129, 61975119, 62305210), the SJTU Pinghu Institute of
Intelligent Optoelectronics (2022SPIOE204), and the Science and Technology on
Metrology and Calibration Laboratory (JLJK2022001B002).

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