In their article, Wang et al. [1] report a new scheme for THz heterodyne detection using a laser-driven LTG-GaAs photomixer [2, 3] and make the impressive claim of achieving near quantum-limited sensitivity at room temperature. Unfortunately, their experimental methodology is incorrect, and furthermore the paper provides no information on the mixer conversion loss, an important quantity that could readily have been measured and reported as a consistency check. The paper thus offers no reliable experimental evidence that substantiates the claimed sensitivities. To the contrary, the very high value reported for their photomixer impedance strongly suggests that the conversion loss is quite poor and that the actual sensitivity is far worse than claimed

Karasik, B.

Kerr, A. R.

Pospieszalski, M.

Zmuidzinas, J.

English

arXiv

Caltech Authors - Main

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Room Temperature, Quantum-Limited THz Heterodyne
Detection? Not Yet
J. Zmuidzinas1, B. Karasik2, A. R. Kerr3, and M. Pospieszalski3
1California Institute of Technology 301-17, 1200 E. California Blvd. ,
Pasadena CA 91125. jonas@caltech.edu
2Jet Propulsion Laboratory 168-314, California Institute of Technology,
4800 Oak Grove Drive, Pasadena CA 91109
3National Radio Astronomy Observatory, 1180 Boxwood Estate Road,
Charlottesville VA 22903
August 1, 2019
Arising from N. Wang et al., Nature Astronomy (2019)
https://doi.org/10.1038/s41550-019-0828-6
In their article, Wang et al. [1] report a new scheme for THz heterodyne detection us-
ing a laser-driven LTG-GaAs photomixer [2, 3] and make the impressive claim of achieving
near quantum-limited sensitivity at room temperature. Unfortunately, their experimental
methodology is incorrect, and furthermore the paper provides no information on the mixer
conversion loss, an important quantity that could readily have been measured and reported
as a consistency check. The paper thus offers no reliable experimental evidence that sub-
stantiates the claimed sensitivities. To the contrary, the very high value reported for their
photomixer impedance strongly suggests that the conversion loss is quite poor and that the
actual sensitivity is far worse than claimed.
THz heterodyne detection has been used in astronomy for over three decades [4] and is
primarily of interest for high-resolution spectroscopy [5]. An illustrative application is the
measurement of rotational transitions of isotopologues of water vapor to estimate the D/H
ratio in comets – indeed, recent data from the SOFIA airborne observatory have reactivated
the debate on whether the water in the Earth’s oceans was delivered by comets [6]. To
date, the best detection sensitivities have been achieved using cryocooled superconducting
devices [5] such as the superconductor-insulator-superconductor (SIS) receivers that enable
ALMA [7] or the hot-electron bolometers (HEB) used in the HIFI instrument on the Herschel
1
Space Observatory [8]. However, other THz space instruments [9] have generally not used
cryocooled detectors due to power, mass, and cost constraints, thereby incurring a sensitivity
penalty of 10× or more. If the sensitivities reported by Wang et al. were correct, this severe
penalty for ambient-temperature operation would be erased and numerous applications would
be enabled.
The sensitivity of a heterodyne receiver is usually reported as a double sideband (DSB)
receiver noise temperature Trec. By definition, Trec is the Rayleigh-Jeans temperature of a
perfect blackbody source that, when illuminating the receiver’s THz-frequency input, would
contribute the same noise power at the output of the final IF amplifier (typically in the GHz
range) as contributed by all of the different components of the THz receiver. The sensitivity
of a heterodyne receiver is subject to the quantum limit [10] arising from the Heisenberg un-
certainty principle, corresponding to Trec ≥ hν/2k for the DSB noise temperature. As shown
in their Figure 3c, the sensitivity claimed by Wang et al. for their room-temperature receiver
lies impressively close to this limit, matching or exceeding the performance of cryocooled SIS
or HEB receivers.
Unfortunately, the experimental procedure used by Wang et al. to measure sensitivity
is fatally flawed. The standard technique for determining the noise temperature is the
“Y -factor” method where the IF noise power PIF is measured using two blackbodies with
different Rayleigh-Jeans temperatures, Thot and Tcold. The Y -factor is the ratio of these two
measurements,
Y =
PIF,hot
PIF,cold
from which the receiver sensitivity is calculated according to
Trec =
Thot − Tcold
Y − 1
− Tcold .
In their Methods section, Wang et al. claim to measure sensitivities “using the standard
Y -factor method”, but this is not the case. In that section, we learn that:
“...the output IF signal at ∼ 1 GHz is detected by a power meter (Mini-Circuits
ZX47-60LN) using a lock-in amplifier with the 100 kHz modulation reference
frequency...”.
The output of the ZX47-60LN power detector [11] is a voltage that responds logarithmically
to the IF power PIF; one could presumably use the measured DC voltage along with a
calibration curve to obtain PIF, as needed for calculation of the Y -factor. However, a lock-in
amplifier does not measure the DC voltage; rather, it measures changes in the voltage that
occur at a 100 kHz rate in response to a modulation. Their Methods section states
“...the optical pump beam from the dual DFB laser system is modulated using
an acousto-optic modulator ... at a 100 kHz rate”
2
meaning that the laser source that drives the photomixer is being turned on and off at the
100 kHz lock-in frequency. Thus, the lock-in reports a quantity that is related to the change
in the IF power that occurs in response to turning the laser on and off, ∆PIF = PIF,on−PIF,off .
Given their statement regarding use of the Y -factor method, Wang et al. presumably take
the ratio of such lock-in readings for hot and cold loads. Although not explicitly stated in
their paper, they apparently make the assumption that the response of their logarithmic
ZX47-60LN detector is linear for small perturbations, in which case taking the ratio yields
Y ′ =
PIF,hot,on − PIF,hot,off
PIF,cold,on − PIF,cold,off
.
This quantity is very different than the standard Y factor. In particular, Y ′ remains invariant
if a constant is added to all power levels, e.g., as a result of a uniform increase of the IF
amplifier noise contribution, whereas Y is definitely not invariant. Furthermore, the paper
makes no mention of measurements of PIF,hot,off or PIF,cold,off , and because this information
is missing, it is not possible to convert the reported values of Y ′ into corrected values for Y .
Noise temperatures calculated using Y ′ are meaningless, and can be radically different from
the true noise temperatures calculated using Y . Thus, one cannot place any confidence in
the sensitivities reported by Wang et al. in their Figure 3c.
What would a properly executed Y -factor measurement reveal about the performance of
their device? Judging from the large photomixer impedance reported by Wang et al., the
sensitivity is likely ∼ 100× worse than claimed. Our argument involves the mixer conversion
loss L, which has a direct impact on receiver sensitivity Trec according to
Trec = Tmixer + LTIF system .
The mixer noise temperature Tmixer cannot be negative, and the noise temperature of the
first-stage low-noise amplifier TLNA sets a lower bound for the noise of the IF system, TIF system.
Thus, Trec ≥ LTLNA must hold. Unfortunately, Wang et al. do not report any values for the
conversion loss L, apparently missing several opportunities for measuring L while collecting
data for their figures 2 and 3. Wang et al. also do not report measurements for TIF system or
TLNA, although according to the manufacturer’s data sheet for their Mini Circuits ZRL-1150
first-stage amplifier [11], we may take TLNA ≥ 70 K as a reasonable value including cable
losses. Thus, the ∼ 150 K noise temperatures reported by Wang et al. at frequencies up to
1 THz require a conversion loss no higher than L ≈ 2, or 3 dB. This is an extremely low
value, comparable to the conversion loss of a well-optimized SIS mixer; if their 300 K mixer
contributes any noise at all, the conversion loss would need to be even lower.
The actual conversion loss is likely ∼ 20 dB worse, as indicated by the photomixer
impedance reported by Wang et al. on page 8 of the supplemental information:
“...RP is the average electrical resistance of the photomixer at a 30 mW pump
power. The estimated RP value from the numerical simulations is in agreement
with the experimentally measured photomixer resistance of 25 kΩ.”
3
This large impedance is in line with data on other LTG-GaAs photomixers including those
previously studied by this group [3]. Thus, there is a severe impedance mismatch between
the 25 kΩ photomixer and the 50Ω IF amplifier, corresponding to a coupling loss of 21 dB.
For the overall conversion loss to be no worse than 3 dB, as required by the reported sensivity,
the photomixer would need to have an internal conversion gain of at least 18 dB! Internal
conversion gain in this device seems implausible, especially such a large value, given the lack
of any measurements of conversion loss and the absence of a clear physical mechanism for
gain.
Indeed, the theory of operation presented by Wang et al. makes no mention of conversion
gain. According to equation (6) of their supplemental information, they assume a linear,
local relationship between the current density ~J and THz electric field ~E at frequency fTHz.
For fTHz < 1/2πτ ≈ 500 GHz where τ = 0.3 ps is the stated carrier lifetime, the response
is essentially instantaneous and their equation (6) is equivalent to Ohm’s law ~J(~r, t) =
σ(~r, t) ~E(~r, t). Here σ(~r, t) is the (real) conductivity that varies with time t and position ~r due
to the photogeneration of carriers by the two lasers with beat frequency fbeat. The equation
~J = σ ~E simply describes current flow in an ordinary resistor, and leads to the circuit version
of Ohm’s law I = V/R, or I(t) = V (t)/R(t) when the conductivity is time dependent. Here
I(t) and V (t) are the current and voltage across the terminals of the THz spiral antenna, and
the R(t) is the time-dependent photomixer resistance as seen from the antenna terminals.
Thus, the theory offered by Wang et al. places the device into a well-known class of “resistive
mixers” that includes diode mixers [12] and FET mixers [13], which are not capable of
conversion gain and in fact are subject to a theoretical minimum conversion loss of 3 dB
[14, 15]. Their theory is therefore incompatible with their claimed sensitivity, which requires
a large internal conversion gain to overcome the severe IF impedance mismatch as discussed
above. While the resistive mixer argument strictly holds only for fTHz < 500 GHz, one
expects photomixer performance to deteriorate at higher frequencies [2], as Wang et al.
themselves state when discussing the utility of the short lifetime τ = 0.3 ps to “recombine
the slow photocarriers that degrade the terahertz-to-RF conversion efficiency”.
We close by offering recommendations the authors could adopt to address our concerns
and to build confidence in their results:
• Eliminate the lock-in and use the standard Y -factor method to determine Trec. It may
be helpful to add IF gain to boost the detector output and to use a square-law IF
detector rather than a logarithmic detector.
• Measure and report the mixer conversion loss, an urgently needed consistency check.
This could be measured during the hot/cold load procedure if the IF system is cali-
brated.
• Measure the noise temperature of the IF system, and estimate the IF contribution to
the receiver noise using the measured conversion loss.
4
• Experimentally demonstrate that the receiver response is truly heterodyne, e.g., by
using infrared-blocking filters, THz passband filters, and ideally gas-cell measurements
of molecular absorption lines.
The research by BK was performed at the Jet Propulsion Laboratory, California Institute
of Technology, under a contract with the National Aeronautics and Space Administration.
The National Radio Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc.
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Room Temperature, Quantum-Limited THz Heterodyne Detection? Not Yet

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