Shai Machnes

Pulsed Laser Cooling for Cavity Optomechanical Resonators

A pulsed cooling scheme for optomechanical systems is presented that is capable of cooling at much faster rates, shorter overall cooling times, and for a wider set of experimental scenarios than is possible by conventional methods. The proposed scheme can be implemented for both strongly and weakly coupled optomechanical systems in both weakly and highly dissipative cavities. We study analytically its underlying working mechanism, which is based on interferometric control of optomechanical interactions, and we demonstrate its efficiency with pulse sequences that are obtained by using methods from optimal control. The short time in which our scheme approaches the optomechanical ground state allows for a significant relaxation of current experimental constraints. Finally, the framework presented here can be used to create a rich variety of optomechanical interactions and hence offers a novel, readily available toolbox for fast optomechanical quantum control.

Superfast laser cooling.

Currently, laser cooling schemes are fundamentally based on the weak coupling regime. This requirement sets the trap frequency as an upper bound to the cooling rate. In this work we present a numerical study that shows the feasibility of cooling in the strong-coupling regime which then allows cooling rates that are faster than the trap frequency with experimentally feasible parameters. The scheme presented here can be applied to trapped atoms or ions as well as to mechanical oscillators. It can also cool medium sized ion chains close to the ground state.

On the relation between Bell's inequalities and nonlocal games

We investigate the relation between Bells inequalities and nonlocal games by presenting a systematic method for their bilateral conversion. In particular, we show that while to any nonlocal game there naturally corresponds a unique Bells inequality, the converse is not true. As an illustration of the method we present a number of nonlocal games that admits better odds when played using quantum resources.

Gradient optimization of analytic controls: the route to high accuracy quantum optimal control

We argue that quantum optimal control can and should be done with analytic control functions, in the vast majority of applications. First, we show that discretizing continuous control functions as piecewise-constant functions prevents high accuracy optimization at reasonable computational costs. Second, we argue that the number of control parameters required is on-par with the dimension of the object manipulated, and therefore one may choose parametrization by other considerations, e.g. experimental suitability and the potential for physical insight into the optimized pulse. Third, we note that optimal control algorithms which make use of the gradient of the goal function with respect to control parameters are generally faster and reach higher final accuracies than non gradient-based methods. Thus, if the gradient can be efficiently computed, it should be used. Fourth, we present a novel way of computing the gradient based on an equation of motion for the gradient, which we evolve in time by the Taylor expansion of the propagator. This allows one to calculate any physically relevant analytic controls to arbitrarily high precision. The combination of the above techniques is GOAT (Gradient Optimization of Analytic conTrols) gradient-based optimal control for analytic control functions, utilizing exact evolution in time of the derivative of the propagator with respect to arbitrary control parameters.Quantum computation places very stringent demands on gate fidelities, and experimental implementations require both the controls and the resultant dynamics to conform to hardware-specific constraints. Superconducting qubits present the additional requirement that pulses must have simple parameterizations, so they can be further calibrated in the experiment, to compensate for uncertainties in system parameters. Other quantum technologies, such as sensing, require extremely high fidelities. We present a novel, conceptually simple and easy-to-implement gradient-based optimal control technique named gradient optimization of analytic controls (GOAT), which satisfies all the above requirements, unlike previous approaches. To demonstrate GOATs capabilities, with emphasis on flexibility and ease of subsequent calibration, we optimize fast coherence-limited pulses for two leading superconducting qubits architectures-flux-tunable transmons and fixed-frequency transmons with tunable couplers.

Transition Decomposition of Quantum Mechanical Evolution

We show that the existence of the family of self-adjoint Lyapunov operators introduced in Strauss (J. Math. Phys. 51:022104, 2010) allows for the decomposition of the state of a quantum mechanical system into two parts: A backward asymptotic component, which is asymptotic to the state of the system in the limit t→−∞ and vanishes at t→∞, and a forward asymptotic component, which is asymptotic to the state of the system in the limit t→∞ and vanishes at t→−∞. We demonstrate the usefulness of this decomposition for the description of resonance phenomena by considering the resonance scattering of a particle off a square barrier potential. We show that the evolution of the backward asymptotic component captures the behavior of the resonance. In particular, it provides a spatial probability distribution for the resonance and exhibits its typical decay law.

Study of a self-adjoint operator indicating the direction of time within standard quantum mechanics

Abstract In [Y. Strauss, Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schrodinger evolution, J. Math. Phys. 51 (2010) 022104] a self-adjoint operator was introduced that has the property that it indicates the direction of time within the framework of standard quantum mechanics, in the sense that as a function of time its expectation value decreases monotonically for any initial state. In this paper we study some of this operatorʼs properties. In particular, we derive its spectrum and generalized eigenstates, and treat the example of the free particle.

Continuous input nonlocal games

We present a family of nonlocal games in which the inputs the players receive are continuous. We study three representative members of the family. For the first two a team sharing quantum correlations (entanglement) has an advantage over any team restricted to classical correlations. We conjecture that this is true for the third member of the family as well.