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arXiv:1103.1324 · IEEE Transactions on Automatic Control

Experimental Demonstration of Coherent Feedback Control on Optical Field Squeezing

S. Iida, M. Yukawa, Hidehiro Yonezawa, N. Yamamoto, A. Furusawa

Published Jul 19, 2012• 108 citations
arXivHTMLPDF

Abstract

Coherent feedback is a non-measurement based, hence a back-action free, method of control for quantum systems. A typical application of this control scheme is squeezing enhancement, a purely non-classical effect in quantum optics. In this technical note we report its first experimental demonstration that well agrees with the theory taking into account time delays and losses in the coherent feedback loop. The results clarify both the benefit and the limitation of coherent feedback control in a practical situation.

DOI
10.1109/tac.2012.2195831

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Coherent feedback is a non-measurement based, hence a back-action free, method of control for quantum systems. A typical application of this control scheme is squeezing enhancement, a purely non-classical effect in quantum optics. In this technical note we report its first experimental demonstration that well agrees with the theory taking into account time delays and losses in the coherent feedback loop. The results clarify both the benefit and the limitation of coherent feedback control in a practical situation.
Quantum coherent feedback control is a measurement-free control method fully preserving quantum coherence. In this paper we show how time-delayed quantum coherent feedback can be used to control the degree of squeezing in the output field of a cavity containing a degenerate parametric oscillator. We focus on the specific situation of Pyragas-type feedback control where time-delayed signals are fed back directly into the quantum system. Our results show how time-delayed feedback can enhance or decrease the degree of squeezing as a function of time delay and feedback strength.
In the conventional picture of quantum feedback control, sensors make measurements on a quantum system, a classical controller processes the results of the measurements, and semi-classical actuators act back on the system to alter its behavior. Quantum measurements are well known to yield probabilistic results and to introduce unavoidable disturbances in the system measured. Accordingly, quantum feedback is traditionally considered to be both probabilistic and destructive. This paper proposes and provides an experimental demonstration of an alternative method for quantum feedback control, in which sensors, controller, and actuators are themselves quantum systems that interact coherently with the system to be controlled. The resulting feedback loop preserves quantum coherence. Such coherent quantum feedback control is deterministic, non-destructive, and can be used to perform actions such as transferring quantum entanglement that are not possible using conventional feedback control of quantum systems. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
In the conventional picture of quantum feedback, control sensors make measurements on a quantum system, a classical controller processes the results of the measurements, and semiclassical actuators act back on the system to alter its behavior. We describe and provide an experimental demonstration of an alternative method for quantum feedback control, in which the sensors, controller, and actuators of conventional feedback control are replaced with quantum systems that interact coherently with the system to be controlled. The resulting control system represents a fully coherent quantum feedback loop.
A coherent feedback scheme is used to enhance the degree of squeezing of the output field in a cavity optomechanical system. In the feedback loop, a beam splitter (BS) plays the roles of both a feedback controller and an input-output port. To realize effective enhancement, the output quadrature should take the same form as the input quadrature, and the system should operate at the deamplification situation in the meantime. This can be realized by choosing an appropriate frequency-dependent phase angle for the generalized quadrature. Additionally, both the transmissivity of the BS and the phase factor induced by time delays in the loop affect optical squeezing. For the fixed frequency, the optimal values of transmissivity and phase factor can be used to achieve the enhanced optical squeezing. The effect of optical losses on squeezing is also discussed. Optical squeezing is degraded by the introduced vacuum noise owing to the inefficient transmission in the loop. We show that the enhancement of squeezing is achievable with the parameters of the current experiments.
The intensity-difference squeezed state is an important concept in quantum optics, which is not only of great significance for fundamental research in quantum physics, but also an important quantum resource in the fields of quantum communication, quantum computing, and quantum precision measurement. The optical parametric amplifier based on atomic four-wave mixing is one of the most effective means to achieve intensity-difference squeezed light. However, due to the absorption loss of atomic vapor in the light field, the output squeezing still needs improving. By feeding the non-classical optical field from the optical parametric amplifier back to the input port, the quantum characteristics of its output optical field can be enhanced. However, the intensity-difference squeezing enhancement from a phase-insensitive amplifier is experimentally realized based on coherent feedback control. The intensity-difference squeezing enhancement of the phase-sensitive amplifier has not been discussed. In this work, a two-port coherent feedback-controlled phase-sensitive amplifier is analyzed theoretically. The dependence of the intensity-difference squeezing, respectively, on the feedback intensity, the intensity gain of the optical parametric amplifier, and the losses of the system are investigated. For the ideal case in which the losses of the system are ignored, infinite squeezing can be achieved by adjusting the strength and phase of feedback. Considering the actual atomic absorption losses, squeezing enhancement can also be achieved over a wide range of intensity gains within a certain feedback intensity range. In addition, the squeezing enhancement is quite efficient for the medium intensity gain range. The intensity-difference squeezing enhancement strongly depends on the absorption loss of atomic vapor. The smaller the absorption loss, the more significant the squeezing enhancement effect is. Furthermore, the experimental feasibility of this scheme is also considered in detail. Our research can provide useful references for achieving high-quality non classical light fields in experiment, which may find applications in quantum information processing and quantum precise measurement.
Classical feedback control and system theory are playing an important role in modelling, controlling and analysing complex devices in many branches of engineering. Recent developments like quantum computers and miniaturisation of existing applications and devices are increasing the importance of the ability to control systems with quantum effects. Efforts have been made recently to extent the simplicity and power of the language of classical control theory to quantum mechanical systems. Within this framework of “Quantum Feedback Networks” we are investigating two problems. The first problem concerns the enhancement of squeezed states. It has been observed that the squeezing effect of squeezing devices can be enhancement by measurement based feedback techniques or use of optical cavities. We are investigating the possibility of feedback enhanced squeezing using coherent feedback control. Considered is a static ideal squeezing devices interacting with a single mode cavity undergoing coherent feedback using a beam splitter. We show that the overall squeezing of the output depends on the beam-splitter’s reflectivity and that we are thus able to enhance the squeezing by choosing an appropriate configuration of the beam-splitter. In the second part we investigate the question of compatibility of a rigorous approach to the adiabatic elimination of some degrees of freedom of a quantum mechanical systems and instantaneous feed-forward and feedback limits for quantum mechanical networks. The commutativity of both limits is not obvious but frequently assumed in quantum optics. We show that both limit procedures are instances of Schur complements and prove the commutativity of both limits by generalising a statement about successive Schur complements.