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AIP conference proceedings

Solvable model of phase-switching quantum feedback

V. A. Tomilin, Leonid V. Il'ichov

Published Jan 1, 2020• 0 citations
Publisher

Abstract

A quantized optical cavity mode controlled by dissipation, squeezed-light source and feedback loop is studied. The feedback is activated by detections of photons leaving the cavity and rapidly shifts the phase of the cavity field by π. The steady-state of the mode and first-order field correlation functions are obtained in closed analytical form and investigated. It appears that the feedback radically modifies the mode's spectrum. It gains asymmetry and its double-peaked structure becomes much more pronounced than in no-feedback case.

DOI
10.1063/5.0011404

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A quantized optical cavity mode controlled by dissipation, squeezed-light source and feedback loop is studied. The feedback is activated by detections of photons leaving the cavity and rapidly shifts the phase of the cavity field by π. The steady-state of the mode and first-order field correlation functions are obtained in closed analytical form and investigated. It appears that the feedback radically modifies the mode's spectrum. It gains asymmetry and its double-peaked structure becomes much more pronounced than in no-feedback case.
We investigate the steady state of quantized monochromatic cavity mode excited by coherent pumping and placed in a feedback loop that changes the mode phase by π upon each detection of the photon that left the cavity. Such type of feedback is used for fighting decoherence of Schröbinger cat states. Results of numerical calculations of the Glauber P -function for different detunings of mode frequency from pumping frequency are presented. Qualitative explanation for certain peculiarities of the behavior of the P -function is provided. We also suggest a simplified model that gives accurate description of the behavior of the system in the case where external coherent pumping is far detuned from the cavity eigenfrequency.
Summary form only given.Decoherence, i.e., the rapid destruction of the phase relation between two quantum states of a system caused by the entanglement of these two states with two different states of the environment, is the main limiting factor for quantum information processing. For this reason, decoherence control is now becoming a rapidly expanding field of investigation. Decoherence control would be particularly useful in high-Q electromagnetic cavities. In fact, one of the few experimental realizations of a quantum gate is the Caltech's quantum phase gate, demonstrating conditional quantum dynamics between polarized modes in a high-finesse optical cavity. Moreover, the progressive decoherence of a mesoscopic Schrodinger cat state has been observed for the first time in the experiment of Brune et al. (1996) where the linear superposition of two coherent states of a field in a microwave cavity, with classically distinct phases, has been generated and detected. Here we propose a photodetection-mediated feedback scheme based on a very simple idea: whenever a photon leaks out from the cavity and is detected by a photodetector, a feedback loop supplies the cavity mode with another photon, using a single ion trapped in the cavity and appropriately shaped laser pulses.
Microcavities are used in a wide range of classical and quantum applications, from precision measurements, laser technologies, to control of mechanical motion. The dissipative photon loss via absorption, ubiquitous in any optical cavity, is known to introduce thermo-optical effects and impose fundamental limits on precision measurements. We reveal that such dissipative photon absorption can lead to a quantum feedback, via in-loop field detection of the absorbed optical field, whose field fluctuations can be squashed or anti-squashed. A closed-loop dissipative quantum feedback to the cavity field arises. This modifies the optical cavity susceptibility and causes excess noise and correlations when performing coherent response and quantum optomechanical measurements. We experimentally observe such unanticipated dissipative dynamics in optomechanical spectroscopy of sideband-cooled optomechanical crystals at cryogenic temperature (∼\sim∼ 8K) and ambient conditions. The dissipative feedback introduces effective modifications to the optical cavity linewidth and the optomechanical scattering rate, and gives rise to excess imprecision noise in the interferometric quantum measurement of mechanical motion. Such dissipative feedback differs fundamentally from a quantum non-demolition feedback, e.g. optical Kerr squeezing. The dissipative feedback itself always results in anti-squeezed out-of-loop optical field, while it can improve the coexisting Kerr squeezing under certain conditions. Our result applies to cavity spectroscopy in both optical and superconducting microwave cavities , and equally applies to any dissipative feedback mechanism of different bandwidth inside the cavity. It has wide-ranging implications for future dissipation engineering, such as dissipation enhanced sideband cooling and Kerr squeezing, quantum frequency conversion, and nonreciprocity in photonic systems.
In this paper, we use the temporal quantum correlations in the photon statistics of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with an accuracy above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the phase space volume occupied by the resonator field, thereby increasing the dependence of its final state on the measured phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly-efficient single photon detectors, it should be of practical interest until technologies for the generation of highly-entangled many-photon states become more readily available.
Utilizing the continuous frequency mode quantization scheme, we study from first principle the efficiency of a feedback scheme that can generate maximally entangled states of two atoms in an optical cavity through their interactions with a single input photon. The spectral function of the photon emitted from the cavity, which will be used as the input of the next round in the feedback process, is obtained analytically. We find that the spectral function of the photon is modified in each round and deviates from the original one. The efficiency of the feedback scheme consequently deteriorates gradually after several rounds of operation.
In this paper, we use the nonlinear generator of dynamics of the individual quantum trajectories of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with a precision above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the dependence of the state of the resonator on the unknown phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly efficient single photon detectors, it should be of practical interest until highly entangled many-photon states become more readily available.