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arXiv:2107.07992 · Physical Review A

Exploring the limits of the generation of nonclassical states of spins coupled to a cavity by optimal control

Quentin Ansel, Dominique Sugny, Bruno Bellomo

Published Apr 26, 2022• 3 citations
arXivHTMLPDF

Abstract

We investigate the generation of nonclassical states of spins coupled to a common cavity by means of a collective driving of the spins. We propose a control strategy using specifically designed series of short coherent and squeezing pulses, which have the key advantage of being experimentally implementable with the state-of-the art techniques. The parameters of the control sequence are found by means of optimization algorithms. We consider the cases of two and four spins, the goal being either to reach a well-defined target state or a state maximizing a measure of nonclassicality. We discuss the influence of cavity damping and spin offset on the generation of nonclassical states. We also explore to what extent squeezing fields help to enhance the efficiency of the control process.

DOI
10.1103/physreva.105.042618

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We investigate the generation of nonclassical states of spins coupled to a common cavity by means of a collective driving of the spins. We propose a control strategy using specifically designed series of short coherent and squeezing pulses, which have the key advantage of being experimentally implementable with the state-of-the art techniques. The parameters of the control sequence are found by means of optimization algorithms. We consider the cases of two and four spins, the goal being either to reach a well-defined target state or a state maximizing a measure of nonclassicality. We discuss the influence of cavity damping and spin offset on the generation of nonclassical states. We also explore to what extent squeezing fields help to enhance the efficiency of the control process.
We consider a pair of coupled spins with Ising interaction in the zzz direction and study the problem of generating efficiently the triplet Bell state. We initially analyze the transitionless quantum driving shortcut to adiabaticity method and point out its limitations when the available duration approaches zero. In this short time limit we explicitly calculate the fidelity of the method and find it to be much lower than unity, no matter how large the available control fields become. We find that there is a lower bound on the necessary time to complete this transfer, set by the finite value of the interaction between the spins. We then use numerical optimal control to find bang-bang pulse sequences, as well as, smooth controls, which can generate high levels of the target Bell state in the minimum possible time. The results of the present work are not restricted only to spin systems, but are expected also to find applications in other physical systems which can be modeled as interacting spins, for example, coupled quantum dots.
Nonadiabatic driving in ultrastrongly coupled light--matter systems is commonly regarded as a source of errors, as counter-rotating interactions convert vacuum fluctuations into real excitations through the dynamical Casimir effect (DCE). Here we show that, instead, the DCE can be harnessed as a resource for engineering nonclassical states of light. Considering a cavity mode ultrastrongly coupled to a frequency-tunable qubit, we employ optimal quantum control to design driving protocols that convert vacuum fluctuations into targeted states. Numerical optimization reveals a versatile and robust approach for the deterministic preparation of a broad class of nonclassical states, illustrated here through Fock states, squeezed states, and Schrödinger-cat-state superpositions.
The dynamics of the driven Jaynes-Cummings model where a two-level atom is coupled to a single mode of cavity fields and is driven by an external coherent field is investigated. We find that in this model quantum collapse and revivals of the atomic population inversion and squeezing of the cavity field can be generated from a thermal photon state. We also notice that the squeezing is very sensitive to the mean number of thermal photons initially in the cavity, but the quantum collapse and revivals are not. The influence of the amplitude of the driving field and various detuning parameters on the nonclassical effects is discussed. The result shows that one can use the external field to control nonclassical effects in the Jaynes-Cummings model.
We consider a pair of coupled spins with Ising interaction in z-direction and study the problem of generating efficiently the triplet Bell state. We initially analyze the transitionless quantum driving shortcut to adiabaticity method and point out its limitations when the available duration approaches zero. In this short time limit we explicitly calculate the fidelity of the method and find it to be much lower than unity, no matter how large the available control fields become. We find that there is a lower bound on the necessary time to complete this transfer, set by the finite value of the interaction between the spins. We then use numerical optimal control to find bang-bang pulse sequences, as well as, smooth controls, which can generate high levels of the target Bell state in the minimum possible time. Finally, we explain how this method can be adapted for the efficient generation of general quantum entanglement in the system. The results of the present work are not restricted only to spin systems, but is expected to find also applications in other physical systems which can be modeled as interacting spins, such as, for example, coupled quantum dots.
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.
Abstract We analyze the generation of spin-squeezed states via coupling of three-level atoms to an optical cavity and continuous quantum measurement of the transmitted cavity field in order to monitor the evolution of the atomic ensemble. Using analytical treatment and microscopic simulations of the dynamics, we show that one can achieve significant spin squeezing, favorably scaling with the number of atoms N. However, contrary to some previous literature, we clarify that it is not possible to obtain Heisenberg scaling without the continuous feedback that is proposed in optimal approaches. In fact, in the adiabatic cavity removal approximation and large N limit, we find the scaling behavior N − 2 / 3 for spin squeezing and N − 1 / 3 for the corresponding protocol duration. These results can be obtained only by considering the curvature of the Bloch sphere, since linearizing the collective spin operators tangentially to its equator yields inaccurate predictions. With full simulations, we characterize how spin-squeezing generation depends on the system parameters and departs from the bad cavity regime, by gradually mixing with cavity-filling dynamics until metrological advantage is lost. Finally, we discuss the relevance of this spin-squeezing protocol to state-of-the-art optical clocks.