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Physical Review A

Feasibility of squeezing measurements with cavity-based atom detection

Rachel Poldy, B. C. Buchler, P. A. Altin, Nicholas P. Robins, J. D. Close

Published Oct 4, 2012• 3 citations
Publisher

Abstract

We numerically analyze the quantum efficiency and dark noise of a cavity-based single-atom detector, with particular emphasis on the ability to measure number squeezing in an atom-laser beam. We consider the influence of the electric-dipole force on an atom in a red-detuned detection beam and discuss the much improved detection efficiency for detuned probe beams, with respect to resonant probes, resulting from this influence. Cavities allow real-time monitoring of atomic flux, with single-atom resolution, but they are much slower than their analog in photonics (the avalanche photodiode), so flux limits must be imposed. The proposed detector operates at a maximum flux of 5000 atoms/second, but with a shot-noise clearance of up to 23 dB, allowing the full advantage afforded by number squeezing to be observed.

DOI
10.1103/physreva.86.043806

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We numerically analyze the quantum efficiency and dark noise of a cavity-based single-atom detector, with particular emphasis on the ability to measure number squeezing in an atom-laser beam. We consider the influence of the electric-dipole force on an atom in a red-detuned detection beam and discuss the much improved detection efficiency for detuned probe beams, with respect to resonant probes, resulting from this influence. Cavities allow real-time monitoring of atomic flux, with single-atom resolution, but they are much slower than their analog in photonics (the avalanche photodiode), so flux limits must be imposed. The proposed detector operates at a maximum flux of 5000 atoms/second, but with a shot-noise clearance of up to 23 dB, allowing the full advantage afforded by number squeezing to be observed.
We present a thorough analysis of single-atom detection using optical cavities. The large set of parameters that influence the signal-to-noise ratio for cavity detection is considered, with an emphasis on detunings, probe power, cavity finesse, and photon detection schemes. Real device operating restrictions for single photon counting modules and standard photodiodes are included in our discussion, with heterodyne detection emerging as the clearly favorable technique, particularly for detuned detection at high power.
Magnetic microtraps for ultracold atoms combine tight confinement, long storage times, high degree of control over the atomic position, and good optical access. Atom detection can be implemented via fluorescence, absorption, or dispersive measurements. All three types of measurements can be enhanced by an optical resonator, where the enhancement factor is proportional to the resonator finesseF. In the limit of negligible detector counts, in a setup where the detector registers n counts per atom in a fluorescence measurement, the atom number resolution is DeltaNf= (N/n)1/2for a fluorescence measurement, and DeltaNa= (1/4N)1/2for an absorption measurement. This means that absorption and fluorescence measurements perform similarly for one atom, but that the absorption measurement is superior for N >1. However, in absorption measurements the number of atoms must remain sufficiently small for the atomic absorption not to deteriorate the resonator finesse. Larger samples can be probed by dispersive measurements, where the tuning of the resonator due to the atomic index of refraction is measured. In the absence of technical noise, the corresponding atom number resolution is independent of detuning from the atomic transition, and given by DeltaNd= (1/n)1/2. Using fluorescence detection in a resonator of finesse F=8000, we detect two counts per atom in 250 mus, enabling single-atom detection with 75% efficiency (Teper et al., 2006). Absorption detection with 3.3% transmission attenuation enables us to measure small samples with up to 10 atoms with a resolution of about one atom. Absorptive and dispersive detection are interesting in that the resolution is not decreased with higher atom number. The reason is that both rely on the forward scattered signal, where the fields emitted by different atoms add coherently. These methods therefore allow non-destructive measurements below the atom-number shot noise, provided that the optical depth of the sample exceeds unity. We have realized an optical depth of several thousand inside the resonator, which should enable trapped-atom detection significantly below the shot-noise limit. If the detection is applied in a state-selective manner to a sample of two-level atoms (Geremia et al., 2004), conditional spin squeezing results. Such squeezing of the pseudo-spin for an atomic clock transition can be used to realize a hyperfine atomic clock on a microchip (Treutlin et al., 2004) that operates below the atom number shot noise limit (standard quantum limit). We report experimental progress towards pseudo-spin squeezing for87Rb atoms trapped on the microchip.
Atom interferometers (AIs) are promising tools for precision measurement with applications ranging from geophysical exploration and tests of the equivalence principle of general relativity to the detection of gravitational waves. Their optimal sensitivity is ultimately limited by their detection noise. We review resonant and near-resonant methods to detect the atom number of the interferometer outputs, and we theoretically analyze the relative influence of various scheme dependent noise sources and the technical challenges affecting the detection. We show that for the typical conditions under which an AI operates, simultaneous fluorescence detection with a charge-coupled device sensor is the optimal imaging scheme. We extract the laser beam parameters such as detuning, intensity, and duration required for reaching the atom shot noise limit.
We report the measurement of the intensity difference squeezing via the non-degenerate four-wave mixing process in a rubidium atomic vapor medium. Two pairs of balanced detection systems are employed to measure the probe and the conjugate beams, respectively. It is convenient to get the quantum shot noise limit, the squeezed and the amplified noise power spectra. We also investigate the influence of the input extra quadrature amplitude noise of the probe beam. The influence of the extra noise can be minimized and the squeezing can be optimized under the proper parameter condition. We measure the −3.7-dB intensity difference squeezing when the probe beam has a 3-dB extra quadrature amplitude noise. This result is slightly smaller than −4.1 dB when the ideal coherent light (no extra noise) for the probe beam is used.
Abstract Among the known resources of quantum metrology, one of the most practical and efficient is squeezing. Squeezed states of atoms and light improve the sensing of the phase, magnetic field, polarization, mechanical displacement. They promise to considerably increase signal-to-noise ratio in imaging and spectroscopy, and are already used in real-life gravitational-wave detectors. But despite being more robust than other states, they are still very fragile, which narrows the scope of their application. In particular, squeezed states are useless in measurements where the detection is inefficient or the noise is high. Here, we experimentally demonstrate a remedy against loss and noise: strong noiseless amplification before detection. This way, we achieve loss-tolerant operation of an interferometer fed with squeezed and coherent light. With only 50% detection efficiency and with noise exceeding the level of squeezed light more than 50 times, we overcome the shot-noise limit by 6 dB. Sub-shot-noise phase sensitivity survives up to 87% loss. Application of this technique to other types of optical sensing and imaging promises a full use of quantum resources in these fields.
Squeezed states of light enable quantum-enhanced measurements but are limited by optical loss, particularly at 2 um where photodiode efficiency is low. We report the first loss-tolerant, audio-band squeezed light detection at 1984 nm by using a phase-sensitive amplifier to amplify the squeezed vacuum prior to detection. This technique increases the effective detection efficiency from 74% to 95% and increases the observed squeezing from 4 dB to 8 dB, the highest level of squeezing observed at this wavelength. Additionally, the shot-to-dark-noise clearance increases, extending the effective measurement bandwidth toward lower frequencies. This approach is largely wavelength-independent, extending high-fidelity quantum measurements to future gravitational-wave detectors and related quantum technologies.