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Journal of Experimental and Theoretical Physics Letters

Quantized optical mode in a phase-switching feedback loop

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

Published Feb 1, 2015• 3 citations
Publisher

Abstract

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.

DOI
10.1134/s0021364014230143

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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.
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.
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.
The interaction of an atom with both a quantized cavity field and an external classical driving field, the fields being degenerate in frequency, is studied in the regime where the atom and fields are highly detuned. The atom interacts dispersively with the quantized field but the classical driving field gives rise to the creation or destruction of photons conditional on the state of the atom. We show how this interaction can be used to generate coherent states of the cavity field and various forms of superpositions of macroscopically distinct states. This method is in contrast to the usual method used in microwave cavity QED of injecting a coherent state into a cavity via a waveguide attached to a klystron and where subsequently Schr\"odinger cat states may be generated by manipulating the field with injected atoms. The method proposed here could possibly be used in the case of an optical cavity. Further, we show that coherent states may be generated in the steady state from the competition between the driven dispersion interaction and dissipative single-photon losses, a form of optical balance.
We propose a cavity quantum electrodynamic system consisting of a five-level atom coupled to a single mode of the cavity electromagnetic field. The study is focused on the regime of strong coupling between the cavity and atom. Pump laser fields and cavity fields connect the split energy levels of the atom. Instead of the well-known two-level Dicke model obtained by adiabatic elimination of the high-energy levels, we consider the pump lasers' detunings to the atomic transitions to be very small such that we can examine the influence of the higher-energy states. We have studied the effect of an external coherent drive and incoherent pumping on these higher-energy levels and observed the enhancement of intracavity photon numbers due to quantum coherence effects. The amplification of intracavity photons is achieved even without a population inversion. However, the effect of the coherent and incoherent drive is negligible for very large detunings when the higher-energy states are adiabatically eliminated. At zero and small detunings, the system reaches the steady state at an earlier instant of time for higher incoherent pumping. We find an almost agreeable steady-state behavior of the system's exact full quantum dynamics model and its semiclassical approximation. Our model tries to accurately simulate the open system by considering the cavity decay, spontaneous decay, and dephasing of the system.
In this proceeding we show how to formulate the quantum stochastic Schrodinger equation (QSSE) of the Jaynes-Cummings-model, where the cavity mode is subject to coherent feedback as control mechanism. We start from the Jaynes-Cummings Hamiltonian and the Hamiltonian for feedback on the cavity mode and derive the QSSE and show how to represent the system state as a matrix product state in order to derive a numerically tractable model for the case of the Jaynes-Cummings model subject to feedback. We compare the dynamics for stabilization of the Rabi oscillation with the solution of the Schrodinger equation in the single excitation regime. Furthermore, we compare this with the behavior for the case with two excitations in the system.