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Quantum Optimal Control for Mixed State Squeezing

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

Published Jul 12, 2018• 0 citations
OpenAlex

Abstract

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.

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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 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.
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.
The efficient initialization of a quantum system is a prerequisite for quantum technological applications. Here we show that several classes of quantum states of a harmonic oscillator can be efficiently prepared by means of a Jaynes-Cummings interaction with a single two-level system. This is achieved by suitably tailoring external fields which drive the dipole and/or the oscillator. The time-dependent dynamics that leads to the target state is identified by means of optimal control theory (OCT) based on Krotov's method. Infidelities below ${10}^{\ensuremath{-}4}$ can be reached for the parameters of the experiment of Raimond, Haroche, Brune and co-workers, where the oscillator is a mode of a high-Q microwave cavity and the dipole is a Rydberg transition of an atom. For this specific situation we analyze the limitations on the fidelity due to parameter fluctuations and identify robust dynamics based on pulses found using ensemble OCT. Our analysis can be extended to quantum-state preparation of continuous-variable systems in other platforms, such as trapped ions and circuit QED.
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.
This paper presents a framework for solving the pure-state preparation problem using numerical optimal control. As an example, we consider the case where a number of qubits are dispersively coupled to a readout cavity. We model open system quantum dynamics using the Markovian Lindblad master equation driven by external control pulses. The main result of this paper develops a basis of density matrices (a parameterization) where each basis element is a density matrix by itself. Utilizing a specific objective function, we show how an ensemble of the basis elements can be used as a single initial state throughout the optimization process—independent of the system dimension. We apply the general framework to the specific application of ground-state reset of one and two qubits coupled to a readout cavity.