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arXiv:1103.0335 · Physical Review Letters

Conditional Spin Squeezing of a Large Ensemble via the Vacuum Rabi Splitting

Zilong Chen, Justin Bohnet, S. Sankar, Jiayan Dai, James K. Thompson

Published Mar 29, 2011• 167 citations
arXivHTMLPDF

Abstract

We use the vacuum Rabi splitting to perform quantum nondemolition measurements that prepare a conditionally spin squeezed state of a collective atomic psuedospin. We infer a 3.4(6) dB improvement in quantum phase estimation relative to the standard quantum limit for a coherent spin state composed of uncorrelated atoms. The measured collective spin is composed of the two-level clock states of nearly 10(6) (87)Rb atoms confined inside a low finesse F=710 optical cavity. This technique may improve atomic sensor precision and/or bandwidth, and may lead to more precise tests of fundamental physics.

DOI
10.1103/physrevlett.106.133601

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We use the vacuum Rabi splitting to perform quantum nondemolition measurements that prepare a conditionally spin squeezed state of a collective atomic psuedospin. We infer a 3.4(6) dB improvement in quantum phase estimation relative to the standard quantum limit for a coherent spin state composed of uncorrelated atoms. The measured collective spin is composed of the two-level clock states of nearly 10(6) (87)Rb atoms confined inside a low finesse F=710 optical cavity. This technique may improve atomic sensor precision and/or bandwidth, and may lead to more precise tests of fundamental physics.
Large ensembles of uncorrelated atoms are extensively used as precise sensors of time, rotation, and gravity, and for tests of fundamental physics. The quantum nature of the sensors imposes a limit on their ultimate precision. Larger ensembles of N atoms can be used to average the quantum noise as 1/√N, a scaling known as the standard quantum limit. However, the ensemble size may be limited by technical constraints and/or atom-atom collisions -- a fundamental distinction from photon-based sensors. Learning to prepare entangled states of large ensembles with noise properties below the standard quantum limit will be key to extending both the precision and/or bandwidth of atomic sensors. More broadly, the generation and application of entanglement to solve problems is a core goal of quantum information science being pursued in both atomic and solid state systems.\nIn this thesis, we utilize the tools of cavity-QED to prepare entangled spin-squeezed states with 3.4(6) dB improvement in spectroscopic sensitivity over the standard quantum limit. The collective atomic spin is composed of the two-level clock states of 87Rb confined in a medium finesse F = 710 optical cavity. We employ cavity-aided quantum non-demolition measurements of the vacuum Rabi splitting to measure and subtract out the quantum projection noise of the collective spin state, preparing states with collective atomic spin projection noise 4.9(6) dB below the projection noise level. The conditionally reduced spin noise combined with the measured 1.5(3) dB reduction in the mean spin length implies a net 3.4(6) dB spectroscopic enhancement or conditional squeezing as defined by the Wineland criterion. Our method does not require single particle addressability and is applied to a spectroscopically large ensemble of N = 7 x 105 atoms using two collective population measurements, with the whole squeezing operation taking ~ 150 μs. The gain in sensitivity is spectroscopically equivalent to the enhancement obtained had we created > 105 pairs of maximally entangled qubits, demonstrating the power of a top-down approach for entangling large ensembles. The nondemolition probing of atomic populations via the vacuum Rabi splitting is also of broad interest for non-destructively reading out a wide variety of both atomic and solid state qubits.
Probing the collective spin state of an ensemble of atoms may provide a means to reduce heating via the photon recoil associated with the measurement and provide a robust, scalable route for preparing highly entangled states with spectroscopic sensitivity below the standard quantum limit for coherent spin states. The collective probing relies on obtaining a very large optical depth that can be effectively increased by placing the ensemble within an optical cavity such that the probe light passes many times through the ensemble. Here we provide expressions for measurement resolution and spectroscopic enhancement in such cavity-aided nondemolition measurements as a function of the cavity detuning. In particular, fundamental limits on spectroscopic enhancements in 87Rb{}^{87}\mathrm{Rb}87Rb are considered.
By allowing a large ensemble of laser cooled and trapped 87Rb atoms to interact collectively with an optical cavity, I have explored two phenomena that may prove useful for enhancing precision measurements: superradiant lasing and spin squeezing.\nSuperradiant lasers have been proposed as future ultrastable optical frequency references, with predicted linewidths < 1 millihertz. These lasers operate in an unusual regime of laser physics where collective emission from an atomic ensemble maps the quantum phase stored in the atoms onto the optical cavity field. I will give an overview of my experimental work using a cold-atom, superradiant Raman laser as a model system to confirm a number of the key predictions concerning superradiant lasing, including the possibility of coherent emission with < 1 intracavity photon on average and greatly reduced sensitivity to cavity frequency noise.\nI also present work using cavity-aided, coherence-preserving measurements of the atomic state population to create entanglement between atoms. The entanglement enables more precise estimation of the quantum phase at the heart of nearly all precision measurements and sensors utilizing quantum objects. By utilizing a cycling transition for the quantum non-demolition probe, we have reduced by several orders of magnitude the measurement induced back-action caused by spontaneous Raman transitions. We directly observe, with no background subtraction, a spin squeezed state with sensitivity to measuring a quantum phase enhanced 10.5 times in variance (i.e. 10.2 dB) beyond the standard quantum limit for an unentangled state. This experimental breakthrough demonstrates that quantum-aided sensing techniques can realize large enough enhancements to have a substantial impact on precision measurements and may aid advances in technology as well as searches for new physics.
Squeezing of collective atomic spins has been shown to improve the sensitivity of atomic clocks and magnetometers to levels significantly below the standard quantum limit. In most cases the requisite atom-atom entanglement has been generated by dispersive interaction with a quantized probe field or by state-dependent collisions in a quantum gas. Such experiments typically use complex multilevel atoms like Rb or Cs, with the relevant interactions designed so that atoms behave like pseudospin-12\frac{1}{2}21​ particles. We demonstrate the viability of spin squeezing for collective spins composed of the physical angular momenta of 106{10}^{6}106 Cs atoms, each in an internal spin-4 hyperfine state. A peak metrological squeezing of at least 5dB is generated by quantum backaction from a dispersive quantum nondemolition (QND) measurement, implemented using a two-color optical probe that minimizes tensor light shifts without sacrificing measurement strength. Other significant developments include the successful application of composite pulse techniques for accurate dynamical control of the collective spin, enabled by broadband suppression of background magnetic fields inside a state-of-the-art magnetic shield. The absence of classical noise allows us to compare the observed quantum projection noise and squeezing to a theoretical model that properly accounts for both the relevant atomic physics and the spatial mode of the collective spin, finding good quantitative agreement and thereby validating its use in other contexts. Our work sets the stage for experiments on quantum feedback, deterministic squeezing, and closed-loop magnetometry. The implementation of real-time feedback may also create an opportunity for new types of quantum simulation, wherein the evolution of a quantum system is conditioned on the outcome of a time-continuous QND measurement. Such a scheme has the potential to access new regimes near the quantum-classical boundary, with opportunities to study long-standing issues related to quantum-classical correspondence in chaotic systems.
We propose a scheme for continuously measuring the evolving quantum phase of a collective spin composed of N pseudospins. Quantum nondemolition measurements of a lossy cavity mode interacting with an atomic ensemble are used to directly probe the phase of the collective atomic spin without converting it into a population difference. Unlike traditional Ramsey measurement sequences, our scheme allows for real-time tracking of time-varying signals. As a bonus, spin-squeezed states develop naturally, providing real-time phase estimation significantly more precise than the standard quantum limit of Δϕ_{SQL}=1/sqrt[N] rad.