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arXiv:1807.04718 · Advanced Quantum Technologies

Quantum Optimal Control for Mixed State Squeezing in Cavity Optomechanics

Daniel Basilewitsch, Christiane P. Koch, Daniel M. Reich

Published Feb 27, 2019• 34 citations
arXivHTMLPDF

Abstract

Abstract The performance of key tasks in quantum technology, such as accurate state preparation, can be maximized by utilizing external controls and deriving their shape with optimal control theory. For non‐pure target states, the performance measure needs to match both the angle and the length of the generalized Bloch vector. A measure based on this simple geometric picture that separates angle and length mismatch into individual terms is introduced and the ensuing optimization framework is applied to maximize squeezing of an optomechanical oscillator at finite temperature. The results herein show that shaping the cavity drives can speed up squeezed state preparation by more than two orders of magnitude. Cooperativities and pulse shapes required to this end are fully compatible with the current experimental technology.

DOI
10.1002/qute.201800110

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Abstract The performance of key tasks in quantum technology, such as accurate state preparation, can be maximized by utilizing external controls and deriving their shape with optimal control theory. For non‐pure target states, the performance measure needs to match both the angle and the length of the generalized Bloch vector. A measure based on this simple geometric picture that separates angle and length mismatch into individual terms is introduced and the ensuing optimization framework is applied to maximize squeezing of an optomechanical oscillator at finite temperature. The results herein show that shaping the cavity drives can speed up squeezed state preparation by more than two orders of magnitude. Cooperativities and pulse shapes required to this end are fully compatible with the current experimental technology.
Accurate state preparation, a key requirement for quantum technology, is often carried out with external controls. In order to obtain maximum performance, the pulse shape of the controls can be derived using optimal control theory, by minimizing a suitable performance measure. Care needs to be taken when defining the performance measure for non-pure target states. Visualizing the open system dynamics on the Bloch sphere, we construct an optimization functional that seeks to independently match Bloch vector angle and length of the target state. We employ the ensuing optimization framework to maximize squeezing of an optomechanical oscillator at finite temperature and find that shaping the cavity drives can significantly speed up squeezed state preparation.
Abstract Cavity optomechanical systems are one of the leading experimental platforms for controlling mechanical motion in the quantum regime. We exemplify that the control over cavity optomechanical systems greatly increases by coupling the cavity also to a two-level system, thereby creating a hybrid optomechanical system. If the two-level system can be driven largely independently of the cavity, we show that the nonlinearity thus introduced enables us to steer the extended system to non-classical target states of the mechanical oscillator with Wigner functions exhibiting significant negative regions. We illustrate how to use optimal control techniques beyond the linear regime to drive the hybrid system from the near ground state into a Fock target state of the mechanical oscillator. We base our numerical optimization on realistic experimental parameters for exemplifying how optimal control enables the preparation of decidedly non-classical target states, where naive control schemes fail. Our results thus pave the way for applying the toolbox of optimal control in hybrid optomechanical systems for generating non-classical mechanical states.
The preparation of mechanical quadrature-squeezed states holds significant importance in cavity optomechanics because the squeezed states have extensive applications in understanding fundamental quantum mechanics and exploiting modern quantum technology. Here, we propose a reliable scheme for generating mechanical quadrature squeezing in a typical cavity optomechanical system via seeking optimal cavity-field driving pulses using the gradient-descent algorithm. We realize strong quadrature squeezing in a mechanical resonator that exceeds the 3-dB steady-state limit, even with a thermal phonon occupancy of 100. Furthermore, the mechanical squeezing can be ultrarapidly created within one mechanical oscillation period. We also obtain the optimal pulsed drivings associated with the created mechanical squeezings and analyze the mechanism for mechanical squeezing generation. This paper will promote the application of optimal quantum control in quantum optics and quantum information science.
Abstract Ideally, the characterization of non-classical states requires measurements on timescales much shorter than the system’s decoherence time. However, in quantum cavity electrodynamics, photon loss rates are often comparable to measurement rates, which degrades the fidelity of the readout. In this work, we propose an active protocol to accelerate the phase estimation of squeezed vacuum states trapped in a lossy cavity. Instead of relying on passive leakage or linear coherent driving, we excite the system with a time-optimized degenerate parametric drive. This adapted two-photon pump actively amplifies the relevant quantum fluctuations, rapidly projecting the phase information of the squeezed state onto the integrated homodyne photocurrent of the output field before significant decoherence occurs. Because a squeezed vacuum carries no phase information in its first moments, this quadratic control is the minimal resource able to imprint the squeezing angle onto the detected signal. Using a numerical optimal control approach, we derive pumping envelopes that maximize the ability to distinguish between orthogonal squeezed states, achieving approximately a 6.02-fold increase in signal contrast compared to constant excitation schemes. We demonstrate that this active extraction protocol produces a strictly monotonic calibration curve, enabling rapid and unambiguous identification of the squeezed phase angle. Furthermore, robustness analysis confirms that the phase estimate remains reliable even in the presence of intense Gaussian detection noise, providing a practical framework for rapid state verification in open-system quantum technologies.
Quantum control technology provides an increasingly useful toolbox for quantum information tasks. In this Letter, by introducing a pulsed coupling to a standard optomechanical system, we show that stronger squeezing can be obtained with pulse modulation due to the reduction of the heating coefficient. Also, the general squeezed states, such as the squeezed vacuum, squeezed coherent, and squeezed cat states, can be obtained with their squeezing level exceeding 3 dB. Moreover, our scheme is robust to cavity decay, thermal temperature, and classical noise, which is friendly to experiments. The present work can extend the application of quantum engineering technology in optomechanical systems.