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# Enhanced Imaging of Electronic Hot Spots Using Quantum Squeezed Light

Haechan An,1,2 Ali Najjar Amiri,2 Dominic P. Goronzy,3 David A. Garcia
Wetten,3 Michael J. Bedzyk,3,4 Ali Shakouri,1 Mark C. Hersam,3,5 and Mahdi
Hosseini1,2<EMAIL_ADDRESS>1Elmore Family School of Electrical and
Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
2Department of Electrical and Computer Engineering and Applied Physics,
Northwestern University, Evanston, Illinois 60208, USA
3Department of Materials Science and Engineering, Northwestern University,
Evanston, Illinois 60208, USA
4Department of Physics and Astronomy, Northwestern University, Evanston,
Illinois 60208, USA
5Department of Chemistry, Northwestern University, Evanston, Illinois 60208,
USA

###### Abstract

Detecting electronic hot spots is important for understanding the heat
dissipation and thermal management of electronic and semiconductor devices.
Optical thermoreflective imaging is being used to perform precise temporal and
spatial imaging of heat on wires and semiconductor materials. We apply quantum
squeezed light to perform thermoreflective imaging on micro-wires, surpassing
the shot-noise limit of classical approaches. We obtain a far-field
temperature sensing accuracy of 42 mK after 50 ms of averaging and show that a
$256\times 256$ pixel image can be constructed with such sensitivity in 10
minutes. We can further obtain single-shot temperature sensing of 1.6 K after
only 10 $\mathrm{\mu s}$ of averaging enabling dynamical study of heat
dissipation. Not only do the quantum images provide accurate spatio-temporal
information about heat distribution, but the measure of quantum correlation
provides additional information, inaccessible by classical techniques, that
can lead to a better understanding of the dynamics. We apply the technique to
both Al and Nb microwires and discuss the applications of the technique in
studying electron dynamics at low temperatures.

††preprint: APS/123-QED

Far-field thermal imaging has broad applications ranging from electrical
inspection [1, 2, 3] to biology [4, 5, 6, 7, 8]. Optical detection of hot
spots and heat distribution in electronics is particularly important for
developing low-power devices and better thermal management. Optical
thermoreflective imaging has been used to obtain thermal images with high
temporal and spatial resolution in both electronics [9, 3] and biological
samples [10]. The technique can also be used to study charge transport [11]
and diffusion [12] in electronics and superconducting materials. The
sensitivity of these classical measurements is fundamentally limited by the
shot noise and can be improved by using higher illumination power. However,
high-power illumination is not an option when light-induced heating can
interfere with measurement or damage the sample. The effect of light-induced
heating in low-temperature electronics [13, 12] and biological samples [14] is
a well-known issue, and more advancements are needed to overcome the signal-
to-noise ratio limit without interfering with the sample’s properties.

Figure 1:  Experimental diagram of the quantum photothermal imaging. The four-
wave mixing process inside a Rb vapor cell is seeded with a probe light that
is amplified at the output leaving the cell together with a correlated
conjugate beam at the opposite sides of the pump. The probe is reflected off
the microwire and detected after polarization rotation using a quarter-wave
plate (QWP) and a polarizing beam splitter (PBS). The difference between the
reflected probe and the directly detected conjugate generates a differential
signal of reflectivity.

Quantum light is known to break the fundamental limits of classical light and
has been proposed in various quantum sensing modalities [15, 16, 17]. In most
scenarios, the single-photon-level quantum light has found little real-world
applications where the threshold power is much higher than a few photons.
Recently, it has been shown that quadrature squeezed states of light can be
used to obtain a true quantum advantage when compared to the best classical
approaches, in very different contexts, improving the detection of
gravitational waves [18, 19] and single-cell imaging [5, 20, 8]. Bright
intensity squeezed states of light [21, 22, 23, 16, 24, 25] are also valuable
resources when considering achieving quantum advantage. This is because these
optical states can be generated at relatively high powers (milliwatt-level
powers) and thus can compete with classical sensing methods applied to certain
applications [26, 24], provided optical losses are relatively small. Even
though applications of squeezed light in various scenarios have been shown [5,
16, 17, 27], quantum imaging with squeezed light has not been demonstrated.

In this article, we utilize intensity-squeezed light for imaging heat in
microwires. We rely on metallic wires’ non-zero thermoreflective coefficient
and sense the temperature by measuring changes in the light’s reflectivity. By
scanning the laser spot across a region of the wire, we are able to construct
images of hot spots in circuits. The metal’s high reflectivity (or low loss)
makes the application of squeezed light particularly relevant to this case.
Because the laser-induced heating is comparable to the temperature sensitivity
limit of the shot-noise-limited measurement, we conclude that there is a
quantum advantage to be gained by using quantum light in this application. To
detect temperature’s effect on quantum light, we use lock-in amplification and
balanced detection. We demonstrate that a two-pixel balanced detection can be
used to generate images as fast as a CCD camera.

Figure 2:  (a) Intensity noise measured on a spectrum analyzer for the quantum
probe-conjugate pair (blue) as well as a coherent laser beam pair (red) shows
intensity squeezing of about 4 dB after reflection compared to the shot-noise
limit (measured by the coherent light). (b) The measured reflection for
multiple hot and cold frames is shown on the top panel, and the lower panel
shows the normalized value of reflectivity averaged over 4000 pulses. The
transient behaviors of temperature during heating and cooling cycles are
modeled by double exponential functions
($a_{0}+a_{1}exp(-t/\tau_{1})+a_{2}exp(-t/\tau_{2})$) and shown by solid red
and blue lines, respectively.

The squeezed light in our experiment is generated via the four-wave mixing
(FWM) process in 85Rb vapor, similar to our previous experiment [24]. Such FWM
process has been used to efficiently generate intensity or quadrature squeezed
light [28, 29]. We use a high-frequency acousto-optic modulator to create a
seed probe beam about 3 GHz away from the pump light, both impinging on a one-
inch vapor cell heated to 106 $\mathrm{{}^{\circ}C}$. Pump and seed probe
beams have powers of 600 mW and 5 $\mathrm{\mu W}$, respectively, detuned from
the D1 transition by about 1.2 GHz. After the cell, a conjugate beam is
generated via the FWM process, whose intensity is correlated to that of the
amplified probe beam exiting the cell. The experimental setup is shown in Fig.
1. The reflected probe light from the wire is detected on a balanced detector
and subtracted from the conjugate beam. The probe beam is scanned across an
area of the sample, and a change in its reflectivity is recorded as a measure
of temperature. The sample’s temperature is modulated by either injecting
current into the Al or Nb circuits or remotely coupling an RF signal to Nb
waveguides. The Al wire is fabricated using photolithography on silicon
dioxide. A thin (5 nm) layer of Ti is deposited on a 300 nm silicon dioxide
layer before depositing 100 nm of Al. Photolithography is used to create
different circuit geometries of Al wires with a typical wire width of 75
$\mathrm{\mu m}$ and connecting bridges of 10-25 $\mathrm{\mu m}$ wide (acting
as hot spots). Coplanar waveguide for the RF circuit is fabricated from a 180
nm Nb film on silicon. For this fabrication, Si(111) was dipped in BOE (5 NH4F
: 1 HF) immediately prior to deposition. Deposition was performed using DC
magnetron sputtering of a 4N8 purity Nb target at 400 W resulting in a
deposition rate of 5 Angstrom/sec. The base pressure of the deposition chamber
was less than 1E-9 Torr. The resulting Nb film was patterned via reactive ion
etching using SF6. Nb coplanar waveguide is patterned as 30 $\mathrm{\mu
m}$-wide center strip placed between ground plates with 18 $\mathrm{\mu m}$
gaps, giving rise to a characteristic impedance of 50 $\Omega$. The metal’s
relative reflectivity $\Delta R/R$ is proportional to the metal’s temperature
change $C_{TR}\Delta T=\Delta R/R$, where $C_{TR}$ is the thermoreflective
coefficient. For a shot-noise-limited light, we have a fundamental
uncertainity of $\delta(\Delta R/R)=1/\sqrt{N}$, where $N$ is the illumination
light’s mean photon number. Squeezed light has less noise compared to shot-
noise-limited light, and it can provide less uncertainty ($\delta(\Delta
R/R)<1/\sqrt{N}$) with the same mean photon number. The active temperature
modulation enables lock-in detection to avoid noise near DC and perform
measurements in a region of the spectrum where the squeezing is optimum (see
Fig. 2 (a)). The temperature modulation of the wire can be controlled by
injecting current pulses or RF signals into the wire. Hot (cold) time-frames
corresponding to current on (off) give rise to an increase (decrease) in the
reflectivity of the probe (see Fig. 2 (b)). The modulation frequency of 40 kHz
has optimum squeezing in the frequency range slow enough for wire to reach the
quasi-thermal saturation.

Figure 3:  (a) Calculated squeezing as a function of gain and conjugate loss
given a 25 % probe loss. (b) Calculated squeezing as a function of the probe
and conjugate loss given a constant gain of 5.

We have a total of 25 % loss of the probe when going through the imaging
system due to the non-unity reflection of the Al wire, scattering, and
polarization losses. The amount of squeezing can be optimized given the losses
on the probe path by controlling the loss of the conjugate and gain of the
probe. The intensity variance is given by the following equation [30]

$V_{loss}=1+2(G-1)\frac{\eta_{p}^{2}G-2\eta_{p}\eta_{c}G+\eta_{c}^{2}(G-1)}{\eta_{p}G+\eta_{c}(G-1)}$
(1)

where $1-\eta_{p}$ and $1-\eta_{c}$ are probe and conjugate loss and $G$ is
the FWM gain. Fig. 3 (a) shows the theoretical plot of variance as a function
of conjugate loss and gain, given a 25 % probe loss in our experiment. The
optimum squeezing at a specific gain is observed by introducing loss on the
conjugate. This is because the probe and conjugate beams individually have
noise above shot noise, and sub-shot-noise intensity is only observed after
subtracting the beams’ intensities. Therefore, loss on one beam means more
uncorrelated noise on the other beam. Fig. 3 (b) depicts variance as a
function of the probe and conjugate loss at an FWM gain of 5. It shows that
probe and conjugate loss should be balanced to achieve optimum squeezing [30].
We adjust the conjugate loss using a polarizing beam splitter. After
optimizing for probe loss in this way, we observe a squeezing of about 4 dB
despite the 25 % probe loss after the cell.

Figure 4:  Microscope images of three different circuits and corresponding
thermal maps obtained using quantum thermoreflective imaging on a section of
the device (dotted box).

Having optimized squeezing for our specific experiment, we carry out imaging
by scanning the probe beam across a region of the wire to map the heat
distribution near regions of high current density (expected hot spots). Fig. 4
shows the heat maps for three different circuit geometries obtained using our
squeezed light. The beam size is only 25 $\mathrm{\mu m}$ in diameter,
limiting the spatial resolution. The spatial resolution can be enhanced simply
using a higher NA lens. Each pixel is averaged for 50 ms to obtain a measure
of its temperature with an accuracy of 42 mK. Squeezing of 3-4 dB is
maintained during the squeezed light scanning. The 2D Galvo mirror is used to
scan the probe beam by 5 $\mathrm{\mu m}$ on the surface of the wire in 0.3
ms, a time duration negligible compared to the single-pixel measurement time.
The probe beam center is scanned to create images with step size smaller than
the probe’s spot size. Fig. 4 (b) & (c) are constructed from $10\times 10$
pixels covering an area of 48 $\mathrm{\mu m}\times$48 $\mathrm{\mu m}$, and
Fig. 4 (a) is an $8\times 8$ pixel image. We note that the probe beam has a
spot size of 25 $\mathrm{\mu m}$, and near the boundaries of the device, the
scattering loss from the tail of the intensity profile limits the imaging
area. In the same way, a $256\times 256$ pixel quantum image with 42 mK
temperature resolution can be constructed in 10 minutes. In our case, the
probe-induced heating is simulated to be less than 20 mK, which is smaller
than the temperature resolution of 42 mK. As a comparison, CCD-based thermal
imaging only reaches a temperature sensitivity of 273 mK during the same
measurement time. Although it can obtain mega-pixel images, a typical CCD has
only a few tens of Hz of frame rate, and this requires a much longer time to
achieve high sensitivity. Our imaging method can have a 66 kilo-pixel image
with 6 times better sensitivity in the same measurement time. Moreover, by
averaging the signal over a single frame (10 $\mathrm{\mu s}$), we can obtain
a temperature resolution of 1.6 K. This is a unique advantage of the balanced
detector, when compared to most CCD cameras with limited frame rates, that
enables tracking fast thermal dynamics in a single measurement. The quantum
source is also capable of generating pulsed squeezed light as low as 50 ns
long [31] to further reduce the laser-induced heating effect and perform the
lock-in detection at different time windows within a thermal cycle.

Figure 5:  (a) Applied voltage to the circuit during the heating and cooling
cycle. (b) Thermal image obtained from quantum thermoreflevtivity sensing,
same as Fig. 4 (c), indicating four regions for which temporal temperature
analysis is performed in (c)-(f). (c)-(f) Temperature change data (dot
symbols) and its error (shaded area) for the heating (red) and cooling (blue)
cycle of four spatial locations in (b). The error bars are obtained by
calculating the standard deviation of the temperature change at different time
steps. The fitting (shown as dashed lines) is done using double exponential
functions ($a_{0}+a_{1}exp(-t/\tau_{1})+a_{2}exp(-t/\tau_{2})$). Insets in
(c)-(f) show the normalized variance calculated from differential intensity of
hot and cold frames.

We can further perform spatial and temporal analysis of the temperature and
heat distribution by measuring the reflectivity during different time windows
after the current is switched on (heating) or off (cooling) for different
spatial locations. Fig. 5 shows the temperature of the device at four
different locations with different proximity from the hot spot as a function
of time during the heating and cooling cycle. It can be seen that near the hot
spot, the temperature is monotonically rising (falling) during the heating
(cooling) cycle. However, away from the hot spot, a plateau region is observed
due to the competition between heating and cooling processes in the device,
namely convection and conduction through different layers. This anomaly is
observed in our images thanks to the enhanced temperature resolution. The
quantum light used in our images has additional degrees of freedom offering
more information about the dynamics of heat dissipation to better understand
this anomaly. Also plotted in Fig. 5 is the variance of differential intensity
of hot and cold frames which represents transient noise response of the
measured raw data. The variance remains within 0.1 dB over the cycle period
showing consistency of measurement noise during hot and cold frames. Moreover,
the time scale of temperature variation is observed to be different near or
away from the hot spot, which is expected to follow a double-exponential
curve. The heat transport through the substrate gives rise to a slow dynamic
of temperature away from the hot spot. We have confirmed the existence of time
scale difference for points close and far from the hot spot using finite-
element simulations. As observed from our simulation, the short current pulses
and the thin SiO2 layer beneath the Al lead to points away from the hot spot
failing to reach thermal equilibrium during the heating-cooling cycle, wherein
various heat transport processes compete. This explains the slow temperature
rise after 5 $\mathrm{\mu s}$, as seen in Fig. 5 (e) and (f), where a double
exponential function is used to fit the data.

The heat dissipation dynamic has shown anomalous signatures at small scales
[32, 33]. The high-resolution temperature sensing and negligible laser-induced
heating offered by quantum light can help further investigate such dynamics.
Akin to fluids, transitioning from laminar flow to turbulence and vortex
formation has been predicted and observed in microelectronics [34, 35]. The
high temperature resolution provided by quantum light can help further our
understanding of fluid-like processes and can aid in designing more efficient
electronic devices, relying on measurement-informed thermal management
approaches.

The study of electron-electron and electron-lattice scattering is more
relevant for materials with large scattering lengths, where vortex formation
in the ballistic or hydrodynamic regimes can be observed. Crystalline Al has
an extremely long momentum relaxation length of about 3.3 mm at around 4.2 K
temperatures [36]. Carrying out similar measurements as those described above
on crystalline Al can be used to study fluid-like dynamics in electronic
devices. Another material that has been recently studied for electron vortex
formation is WTe2, with large scattering lengths at 4.5 K [35]. Nb is another
interesting material used to build superconducting quantum qubits, and
understanding defects and charge (or quasi-particle) density fluctuation in
these materials can lead to developing better materials and devices with long
coherence times [37]. These materials, when measured at low temperatures, are
more susceptible to laser heating, and thus quantum sensing can prove to be a
valuable tool for studying the physics of these quantum materials, in the far
field. To show the feasibility of our quantum sensing technique for Nb, we
also measured thermoreflectivity sensing in a Nb coplanar waveguide subject to
either current or RF radiation from a horn antenna (see Fig. 6 (a)).
Modulation of RF frequency at 3.6 GHz causes modulation of temperature and
thus reflectivity (see Fig. 6 (c)). Even though the thermoreflective
coefficient of Nb is about 50 % smaller than Al at 800 nm [38], we were able
to perform quantum temperature sensing using the same setup for Al wire
measurement. The optical loss of Nb is larger than Al, leading to smaller
squeezing measured after reflection (1-2 dB). Further improvement of squeezing
can be done by adjusting FWM conditions and optimizing the optical gain and
loss of our setup. Moreover, the intrinsic multi-spatial-mode nature of
squeezed light [39, 40, 41, 42] offers possibility of multimode sensing with
cameras [43].

Figure 6:  (a) A top-view microscope image and a schematiccross-section view
of the Nb wire structure are shown on the left. Two different configurations,
DC and RF, for exciting the Nb wire are also depicted on the right.
Thermoreflectivity sensing measurement of a Nb wire of width 30 $\mathrm{\mu
m}$ excited by (b) a DC current and (c) a 3.6 GHz RF tone from a horn antenna
is shown. The thermoreflective coefficient of the Nb wire is assumed to be
$0.9\times 10^{-4}$ K [38], and the temperature change is calculated
accordingly. The change in the reflection of quantum light during the cooling
(blue) and heating (red) cycle corresponds to the change in the temperature of
the sample, with the error bars shown as shaded areas around the curves. The
fitting (shown as dashed lines) is done using double exponential functions
($a_{0}+a_{1}exp(-t/\tau_{1})+a_{2}exp(-t/\tau_{2})$). Insets in (c)-(f) show
the normalized variance calculated from differential intensity of hot and cold
frames.

In conclusion, we utilized quantum intensity-squeezed light to demonstrate the
first quantum thermal imaging of hot spots and heat transport in electronics.
We demonstrated that using quantum light for hot spot detection provides more
details about the dynamics of heat dissipation compared to conventional
optical or electronic techniques [44, 45, 46], thereby enhancing our
understanding of thermal processes in electronics. We applied the imaging
technique to both Al and Nb circuits with a temperature sensing resolution of
42 mK. The quantum thermoreflective imaging described above can be used to
more accurately detect electronic hot spots and heat distribution, study
fundamental properties of superconductors by monitoring quasi-particle
dynamics [47], hydrodynamic and ballistic effects of electron fluid in metals
[35, 11], time and frequency domain thermoreflectance to measure thermal
conductivity, volumetric heat capacity, thermal transport properties, and
electron-phonon coupling in metals [13, 12].

###### Acknowledgements.

We thank Venkat Chandrasekhar for enlightening discussions. We acknowledge
funding from the National Science Foundation CAREER Award number: 2144356 and
DoD-NDEP Award number HQ0034-21-1-0014. The Nb sample preparation was
supported by the U.S. Department of Energy, Office of Science, National
Quantum Information Science Research Centers, Superconducting Quantum
Materials and System Center (SQMS) under Contract No. DE-AC02-07CH11359. This
work made use of the NUFAB Facility, which is supported by the MRSEC program
of the National Science Foundation (DMR-2308691) at the Materials Research
Center of Northwestern University and the Soft and Hybrid Nanotechnology
Experimental Resource (NSF ECCS-2025633).

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