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arXiv:1301.1016 · Physical Review Letters

Unconditional Quantum-Noise Suppression via Measurement-Based Quantum Feedback

Ryotaro Inoue, Shin-Ichi-Ro Tanaka, Ryo Namiki, Takahiro Sagawa, Yoshiro Takahashi

Published Apr 15, 2013• 70 citations
arXivHTMLPDF

Abstract

We demonstrate unconditional quantum-noise suppression in a collective spin system via feedback control based on quantum nondemolition measurement. We perform shot-noise limited collective spin measurements on an ensemble of 3.7×10(5) laser-cooled (171)Yb atoms in their spin-1/2 ground states. Correlation between two sequential quantum nondemolition measurements indicates -0.80(-0.12)(+0.11) dB quantum-noise suppression in a conditional manner. Our feedback control successfully converts the conditional quantum-noise suppression into the unconditional one without significant loss of the noise reduction level.

DOI
10.1103/physrevlett.110.163602

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We demonstrate unconditional quantum-noise suppression in a collective spin system via feedback control based on quantum nondemolition measurement. We perform shot-noise limited collective spin measurements on an ensemble of 3.7×10(5) laser-cooled (171)Yb atoms in their spin-1/2 ground states. Correlation between two sequential quantum nondemolition measurements indicates -0.80(-0.12)(+0.11) dB quantum-noise suppression in a conditional manner. Our feedback control successfully converts the conditional quantum-noise suppression into the unconditional one without significant loss of the noise reduction level.
We apply entropy removal by measurement and feedback to a cold atomic spin ensemble. Using quantum nondemolition probing by Faraday rotation measurement, and feedback by weak optical pumping, we drive the initially random collective spin variable F toward the origin F=0. We use input-output relations and ensemble quantum noise models to describe this quantum control process and identify an optimal two-round control procedure. We observe 12 dB of spin noise reduction, or a factor-of-63 reduction in phase-space volume. The method offers a nonthermal route to generation of exotic entangled states in ultracold gases, including macroscopic singlet states and strongly correlated states of quantum lattice gases.
We demonstrate spin squeezing and entanglement in a large-spin system via quantum non-demolition measurement. We make non-destructive, projection-noise-limited collective spin measurements on an ensemble of up to in 8.4 × 105 laser-cooled 87Rb atoms in the f = 1 hyperfine ground state. A dynamically-decoupled probing scheme [Phys. Rev. Lett. 105, 093602 (2010)] prevents probe-induced decoherence. Repeated measurements show correlations beyond the standard quantum limit, indicating generation of a spin-squeezed state with up to −3.6 dB of noise reduction and −2.6 dB of metrologically-relevant squeezing.
We discuss the theory and experimental considerations of a quantum feedback scheme for producing deterministically reproducible spin squeezing. Continuous nondemolition atom number measurement from monitoring a probe field conditionally squeezes the sample. Simultaneous feedback of the measurement results controls the quantum state such that the squeezing becomes unconditional. We find that for very strong cavity coupling and a limited number of atoms, the theoretical squeezing approaches the Heisenberg limit. Strong squeezing will still be produced at weaker coupling and even in free space (thus presenting a simple experimental test for quantum feedback). The measurement and feedback can be stopped at any time, thereby freezing the sample with a desired amount of squeezing.
The field of quantum metrology concerns the physical measurement of sensors with a precision comparable to fundamental limits set by quantum mechanics. It is possible to outperform naive interpretations of these limits by using entangled states of the sensor system. One example is that of a spin-squeezed state, in which the uncertainty of one variable is decreased at the expense of another while still obeying Heisenberg's uncertainty principle, improving rotation sensitivity along a chosen axis. These states are potentially useful in devices including atomic clocks, inertial sensors, and magnetometers. Any model of a quantum metrology device must respect the fact that physical measurements are not passive, as imagined classically, but necessarily invasive. Far from being a negative feature, well-understood quantum measurement can conditionally drive a system into desirable entangled states, including spin-squeezed states. Furthermore, the fundamental randomness of this process can, in principle, be removed with real-time feedback control, motivating an adaptation of classical feedback concepts to the quantum realm. In this thesis, I describe these ideas in the context of one experimental example. A laser-cooled cloud of cesium spins is polarized along one axis via optical pumping and, subsequently, a linearly polarized far-off resonant probe beam traverses the sample. Due to the interaction Hamiltonian, the optical polarization rotates by an amount nominally proportional to one spin component of the collective spin state, enacting a weak, continuous, nondemolition measurement of that collective variable. This optical Faraday rotation is then measured with a polarimeter and the inherently noisy result used to condition the collective atomic state via a quantum filter, or stochastic master equation. Ideally, this process is capable of producing spin-squeezed states via the measurement itself. The details of this measurement are investigated in depth, including a derivation of the nonideal polarizability Hamiltonian, an analysis of the projection process with control, and a derivation of the magnetometry sensitivity. Experimentally, we demonstrate continuous measurement of the collective spin state with a large single-shot signal-to-noise ratio and verify many predictions of the model. Finally, we describe attempts to observe the atomic projection noise, which would infer the preparation of spin-squeezed states.