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European Quantum Electronics Conference (EQEC)

Quantum theory of continuous photodetection in the presence of feedback

D. B. Horoshko, S. Ya. Kilin

Published Aug 24, 2005• 0 citations
Publisher
DOI
10.1109/eqec.1994.698513

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The usual formulations of the quantum and semiclassical theories of photodetection presume open-loop configurations, i.e., that there are no feedback paths leading from the output of the photodetector to the light beam impinging on that detector. In such configurations, the qualitative and quantitative distinctions between the quantum and semiclassical theories are well understood. In the quantum theory, photocurrent and photocount randomness arises from the quantum noise in the illumination beam, whereas in the semiclassical theory the fundamental source of randomness is associated with the excitations of the atoms forming the detector. Nevertheless, the quantum theory subsumes the semiclassical theory in a natural way.1

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FEEDBACK IN OPEN QUANTUM SYSTEMS

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Open quantum systems continually lose information to their surroundings. In some cases this information can be readily retrieved from the environment and put to good use by engineering a feedback loop to control the system dynamics. Two cases are distinguished: one where the feedback mechanism involves a measurement of the environment, and the other where no measurement is made. It is shown that the latter case can always replicate the former, but not vice versa. This emphasizes the quantum nature of the information being fed back. Two approaches are used to describe the feedback: quantum trajectories (which apply only for feedback based on measurement) and quantum Langevin equations (which can be used in either case), and the results are shown to be equivalent. The obvious applications for the theory are in quantum optics, where the information is lost by radiation damping and can be retrieved by photodetection. A few examples are discussed, one of which is particularly interesting as it has no classical counterpart.

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Incoherent quantum feedback control of collective light scattering by Bose-Einstein condensates

D. A. Ivanov, T. Yu. Ivanova, Igor B. Mekhov

It is well known that in the presence of a ring cavity the light scattering from a uniform atomic ensemble can become unstable resulting in the collective atomic recoil lasing. This is the result of a positive feedback due to the cavity. We propose to add an additional electronic feedback loop based on the photodetection of the scattered light. The advantage is a great flexibility in choosing the feedback algorithm, since manipulations with electric signals are very well developed. In this paper we address the application of such a feedback to atoms in the Bose-Einstein condensed state and explore the quantum noise due to the incoherent feedback action. We show that although the feedback based on the photodetection does not change the local stability of the initial uniform distribution with respect to small disturbances, it reduces the region of attraction of the uniform equilibrium. The feedback-induced nonlinearity enables quantum fluctuations to bring the system out of the stability region and cause an exponential growth even if the uniform state is globally stable without the feedback. Using numerical solution of the feedback master equation we show that there is no feedback-induced noise in the quadratures of the excited atomic and light modes. The feedback loop, however, introduces additional noise into the number of quanta of these modes. Importantly, the feedback opens an opportunity to position the modulated BEC inside a cavity as well as tune the phase of scattered light. This can find applications in precision measurements and quantum simulations.

arXiv:1601.02230•Jan 10, 2016•2 citations
The usual formulations of the quantum and semiclassical theories of photodetection presume open-loop configurations, i.e., that there are no feedback paths leading from the output of the photodetector to the light beam impinging on that detector. In such configurations, the qualitative and quantitative distinctions between the quantum and semiclassical theories are well understood. In the quantum theory, photocurrent and photocount randomness arises from the quantum noise in the illumination beam, whereas in the semiclassical theory the fundamental source of randomness is associated with the excitations of the atoms forming the detector. Nevertheless, the quantum theory subsumes the semiclassical theory in a natural way.1
Open quantum systems continually lose information to their surroundings. In some cases this information can be readily retrieved from the environment and put to good use by engineering a feedback loop to control the system dynamics. Two cases are distinguished: one where the feedback mechanism involves a measurement of the environment, and the other where no measurement is made. It is shown that the latter case can always replicate the former, but not vice versa. This emphasizes the quantum nature of the information being fed back. Two approaches are used to describe the feedback: quantum trajectories (which apply only for feedback based on measurement) and quantum Langevin equations (which can be used in either case), and the results are shown to be equivalent. The obvious applications for the theory are in quantum optics, where the information is lost by radiation damping and can be retrieved by photodetection. A few examples are discussed, one of which is particularly interesting as it has no classical counterpart.
It is well known that in the presence of a ring cavity the light scattering from a uniform atomic ensemble can become unstable resulting in the collective atomic recoil lasing. This is the result of a positive feedback due to the cavity. We propose to add an additional electronic feedback loop based on the photodetection of the scattered light. The advantage is a great flexibility in choosing the feedback algorithm, since manipulations with electric signals are very well developed. In this paper we address the application of such a feedback to atoms in the Bose-Einstein condensed state and explore the quantum noise due to the incoherent feedback action. We show that although the feedback based on the photodetection does not change the local stability of the initial uniform distribution with respect to small disturbances, it reduces the region of attraction of the uniform equilibrium. The feedback-induced nonlinearity enables quantum fluctuations to bring the system out of the stability region and cause an exponential growth even if the uniform state is globally stable without the feedback. Using numerical solution of the feedback master equation we show that there is no feedback-induced noise in the quadratures of the excited atomic and light modes. The feedback loop, however, introduces additional noise into the number of quanta of these modes. Importantly, the feedback opens an opportunity to position the modulated BEC inside a cavity as well as tune the phase of scattered light. This can find applications in precision measurements and quantum simulations.