SUPERCONDUCTING PHOTON NUMBER ...

SUPERCONDUCTING PHOTON NUMBER RESOLVING DETECTORS: PERFORMANCE AND PROMISE Aaron J. Miller1 , Adriana Lita2 , Danna Rosenberg3 , Stephen Gruber2 , and Sae Woo Nam2 1

Department of Physics and Astronomy, Albion College 611 East Porter Street, Albion, Michigan 49224, USA 2 National Institute of Standards and Technology† 325 Broadway Street, Boulder, Colorado 80305, USA 3 Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA The recent rapid progress in the field of novel photon counting detectors has been motivated primarily by the demanding detection requirements of quantum information applications. These applications include long-distance quantum key distribution (QKD) [1, 2], photon source and detector calibration [3], n-photon state quantum-optics experiments [4], and even the potential of photon-based quantum computing [5]. In this paper we present the current state-of-the-art on our superconducting photon detector research with emphasis on microcalorimeter-based superconducting transition-edge sensor (TES) photon number resolving (PNR) detectors. We conclude with a measurement and discussion of background-limited single-photon detection and the fundamental limits to counting noise for any single photon detector–limits that exist even if one were to obtain the “perfect counter”, e.g. as alluded to by Brassard et al.[6]

1.

PERFORMANCE

Optical photon detectors based on superconducting technologies were originally developed and demonstrated as low-resolving-power spectroscopic photon counters for observational astronomy [7,8]. At the cryogenic operating temperatures for such devices (usually significantly below 1 K) the low thermal noise, low material thermal conductances, and zero dc-resistance wiring combine with the favorable qualities of superconductors that give large changes in device resistance or current based on an input in energy. This combination has enabled superconducting photon detectors to outperform all other competing technologies in applications requiring photon-by-photon energy discrimination or applications requiring low detector noise (dark counts). The first application of superconducting detectors to the field of quantum optics or quantum information occurred in 2003 in collaboration between the National Institute of Standards and Technology (NIST, Boulder CO) and Boston University [9]. In this application, and similar one- and two-photon discrimination applications, the incoming photons have an energy Eγ many times larger than the noise level of the detectors. Furthermore, the photons are nearly monochromatic. As a result, the difference in the detector output signal between one- and two-photon absorption is many standard deviations. This high signal-to-noise enables very good discrimination between an absorbed energy of Eγ or †

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2Eγ . At near-infrared wavelengths the discrimination ability is not as high as at optical wavelengths because the energy of the photons decreases but the device noise level does not. In the past the discrimination in the infrared has been sufficient for demonstrations of multiphoton discrimination [10]. However, recent devices now show negligible photonnumber “crosstalk” for absorbed photons, as seen by the excellent separation between the one-, two-, and three-photon absorption peaks in Fig. 1, labeled Eγ1 through Eγ3 , respectively. Practically, however, though the device intrinsically does not have any loss mechanism once a photon is absorbed (that is, a 100% efficiency for absorbed photons), the finite quantum efficiency (QE) of the device causes significant degradation of any input photon number distribution. Given a single-photon QE of η, where 0 ≤ η ≤ 1, the n-photon QE is η n . Therefore, observing an n-photon absorption event becomes strongly dependent on the QE for increasing values of n. As a result, a major effort in improving the NIST TES photon number resolving detectors has been to increase the overall detection efficiency. The two components that comprise the system detection efficiency are the device QE and the optical coupling efficiency. The device QE is maximized by designing device structures that include an integrated low-Q thin-film cavity to enhance absorption of light into the active device material [11]. Film stacks have been demonstrated with absorption of 99% at a target wavelength (or wavelengths) limited only by the complexity of the thin-film cavity design. These multilayer thin-film cavities can be designed to be optimal at any wavelength from the near-ultraviolet through the near-infrared. Through design and material improvements we expect to achieve a (single-photon) device quantum efficiency of 99% at any target wavelength in this band. To ensure a minimum of loss in coupling optical fiber to the devices we pay particular attention to the fiber-to-detector packaging and alignment. Currently the fibers used are low-loss single-mode telecom fibers with a mode field diameter that is approximately 10 µm. The devices are designed to have an active area of 20 µm×20 µm to ensure that all of the light exiting the fiber falls on the device sensitive area. These considerations, along with careful thermal design of the device packaging and anti-reflection coated fibers, we have achieved an end-to-end system efficiency of ∼89% at λ = 1550 nm [12]. A significant problem in single photon detectors used in quantum information applications is the presence of dark counts. The problem of dark counts is particularly acute for applications in which the source has the property of a low photon generation probability (e.g., multiphoton entanglement) or the property of generating photons randomly in time (“unclocked”, cw, or non-pulsed). In fact, both of these source properties are often found in the sources used in quantum information experiments. Superconducting PNR detectors have been demonstrated to exhibit a dark count rate that is unmeasurably low when operated in a fully dark environment [12]. The most recent generation of these high signal-to-noise TES photon counters run in a fully dark cryogenic environment (non-fiber-coupled device) should in principle achieve negligibly low device-induced dark count rates. However, when the detectors are coupled via fiber to a room-temperature experiment, practically achieving such low rates is impossible. In practice, whenever the devices are coupled to a fiber the measured background count rate is several orders of magnitude higher than the theoretical expectations for the dark-count rate. Even when the room-temperature end of the fiber is place into a completely dark

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Figure 1: Histogram showing number of detected photons as a function of energy from a temperature-controlled cavity coupled to a tungsten transition-edge sensor via singlemode telecommunication fiber. The solid curves show the received blackbody photons for temperatures from 0◦ C through 70◦ C in steps of 10◦ C (from low count to high count) and has a bin width of 6.42 meV. The dashed curve shows the histogram of counts from a pulsed 1550 nm laser (bin width of 3.21 meV) used for calibration of the energy scale. environment, hundreds to thousands of photons per second are seen on the detectors. These photons were confirmed to be coming from the high-energy tail of the black-body distribution for the 300 K environment of the fiber end. 2.

BACKGROUND-LIMITED PHOTON COUNTING

To study the rate of background photons as a function of source temperature we connected the room-temperature end of the fiber into an optically-tight temperaturecontrolled laser diode module. With the laser unpowered (always off), the laser diode acts as a temperature-controlled source of blackbody-emitted photons. The laser module (i.e., the source “cavity”) temperature was adjusted and the photon count rate was measured. Fig. 1 shows histograms of detected photons for the temperature-controlled cavity at temperatures from 0◦ C through 70◦ C (in steps of 10◦ C) superimposed on a histogram of a pulsed 1550 nm laser diode. The pulsed laser histogram was used to calibrate the energy scale by noting the positions of the 1-photon, 2-photon, and 3-photon absorption peaks. As seen in Fig. 1, the energy of the blackbody photons does not measurably change as a function of temperature, but the rate of blackbody photons increases with increasing cavity temperature. The total photon rate in the blackbody peak as a function temperature is shown in Fig. 2 fit to the expected photon count rate.

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Figure 2: Total integrated counts received from the temperature controlled cavity as a function of temperature (circles) and the one-dimensional blackbody model (dashed line) as given in Eq. (2). The inset shows the residual from the fit with error bars marking the expected 2σ statistical errors. The expected photon count rate is calculated according to the typical blackbody radiation derivation as given, for example, in Reif [13] with appropriate modification for single-mode blackbody cavity. In this modification the cavity at temperature T is assumed to couple to the fiber only in one dimension and only to the two allowed modes, one for each polarization. Let f (k) dk be the mean number of photons per unit length 1 dk of these with a single polarization and a wave vector between k and k +dk. There are 2π photon states per unit length of our cavity. Furthermore, the mean number of photons with one specific value of k in this range is given by the typical mode population function n=

1 eEγ /kB T

−1

where Eγ = hc/λ = h ¯ ω is the photon energy. Therefore, the mean rate at which photons populate the cavity per unit time (including both allowed polarizations) with an angular frequency between ω and ω + dω, where ω = ck, becomes r(ω)dω =

η dω . h ¯ ω/k BT − 1 πe

(1)

In Eq. (1) we have multiplied by the scale factor η that is the product of the non-unity emissivity of the cavity and the non-unity detection efficiency of the detector. In this model we assumed that η is energy (wavelength) independent. Finally, to get the total expected detection rate across all allowed wavelengths we perform an integration assuming that for wavelengths shorter than a fixed long-wavelength

absorption edge, λ0 , the fiber perfectly transmits and for longer wavelengths it is a cold (i.e., non-radiative) absorber. This integral can be performed easily by making the good assumption that Eγ  kB T . The result of this integration is the mean detector count rate due to blackbody background given by ¯ = ηkB T e−hc/λ0 kB T . (2) R h ¯π The long-wavelength absorption edge of the fiber, λ0 = 1966 nm, was obtained experimentally from the centroid of the blackbody peak shown in Fig. 1. The dashed line in Fig. 2 is the result of least-squares fit to Eq. (2) with a single free parameter η and results in η = 0.15. The inset to the figure shows the residual deviation between the model and the data along with the 2σ statistical error bars. 3.

CONCLUSIONS

These results indicate that care must be taken to ensure that low count-rate experiments are not limited by the residual background photon rate from high-emissivity room temperature optical elements such as long lengths of lossy fiber, absorptive optics and absorption filters. To minimize the background photon flux it is also clearly beneficial to perform narrow wavelength filtering by using cold (non-radiative) optics or by using filters that are reflective so that the cold detector “sees” itself (cold) for wavelengths outside of the signal passband. In the case of even perfect narrow-band filtering, the lowest possible dark count rate can be determined by using Eq. (1) assuming constant rate over small dω. For example, this fundamental dark count limit for T = 300 K and η = 1 gives a rate of ∼0.01 photons/second in a 1 nm bandwidth window at a wavelength of λ =1550 nm. Although the fundamental count-rate limits presented here seem low, already in lownoise broadband devices (with an acceptance window of hundreds of nanometers) this thermal background is the limiting factor in performing low-rate quantum information and quantum optics experiments. Furthermore, while narrowband optical filtering can reduce the thermal background, not all experiments are able to work with narrow optical bandwidth. For example experiments using transform-limited fast pulses sometimes require very large optical bandwidths for the detectors and the thermal background is likely to be non-negligible if these experiments require detection into the near-infrared. The promise for the quantum information sciences given by superconducting devices is still great, and is even more encouraging as newer high-efficiency and higher-speed technologies emerge. However even a perfect detector is limited by fundamental background noise that arises from the thermal background. As future quantum information experiments place demanding requirements on the detector properties, careful thought must be given to ensure that the available detector technologies are well matched to the target wavelength, optical bandwidth, and photon count rate of the experiment. ACKNOWLEDGMENTS We thank the organizers of the QCMC conference for the invitation to present these results. We also thank the U.S. Department of Commerce, DARPA, ARDA, and Albion College for their financial support of this work.

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