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Register a new userNonadiabatic quantum state engineering driven by fast quench dynamics
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There are a number of tasks in quantum information science that exploit non-transitional adiabatic dynamics. Such a dynamics is bounded by the adiabatic theorem, which naturally imposes a speed limit in the evolution of quantum systems. Here, we investigate an approach for quantum state engineering exploiting a shortcut to the adiabatic evolution, which is based on rapid quenches in a continuous-time Hamiltonian evolution. In particular, this procedure is able to provide state preparation faster than the adiabatic brachistochrone. Remarkably, the evolution time in this approach is shown to be ultimately limited by its thermodynamical cost,provided in terms of the average work rate (average power) of the quench process. We illustrate this result in a scenario that can be experimentally implemented in a nuclear magnetic resonance setup.
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Multi-photon quantum interference is the underlying principle for optical quantum information processing protocols. Indistinguishability is the key to quantum interference. Therefore, the success of many protocols in optical quantum information processing relies on the availability of photon states with a well-defined spatial and temporal mode. Photons in single spatial mode can be obtained from nonlinear processes in single-mode waveguides. For the temporal mode, the common approach is to engineer the nonlinear processes. But it is complicated because the spectral properties and the nonlinear interaction are often intertwined through phase matching condition. In this paper, we study a different approach which is based on an SU(1,1) nonlinear interferometer with a pulsed pump and a controllable linear spectral phase shift for precise engineering. We systematically analyze the important figures of merit such as modal purity and heralding efficiency to investigate the feasibility of this approach. Specifically, we analyze in detail the requirement on the spectral phase engineering to optimize the figures of merit and apply numerical simulations to a fiber system. Both modal purity and efficiency are improved simultaneously. Furthermore, a novel multi-stage nonlinear interferometer is proposed and shown to achieve more precise state engineering for near-ideal single-mode operation and near-unity efficiency. We also extend the study to the case of high gain in the four-wave mixing process for the spectral engineering of quantum entanglement in continuous variables. Our investigation provides a new approach for precisely tailoring the spectral property of quantum light sources, especially, photon pairs can be engineered to simultaneously possess the features of high purity, high collection efficiency, high brightness, and high flexibility in wavelength and bandwidth selection.
We introduce a simple yet versatile protocol to inverse engineer the time-dependent Hamiltonian in two- and three level systems. In the protocol, by utilizing a universal SU(2) transformation, a given speedup goal can be obtained with large freedom to select the control parameters. As an illustration example, the protocol is applied to perform population transfer between nitrogen-vacancy (NV) centers in diamond. Numerical simulation shows that the speed of the present protocol is fast compared with that of the adiabatic process. Moreover, the protocol is also tolerant to decoherence and experimental parameter fluctuations. Therefore, the protocol may be useful for designing an experimental feasible Hamiltonian to engineer a quantum system.
We address quantum state engineering of single- and two-mode states by means of non-deterministic noiseless linear amplifiers (NLAs) acting on Gaussian states. In particular, we show that NLAs provide an effective scheme to generate highly non-Gaussian and non-classical states. Additionally, we show that the amplification of a two-mode squeezed vacuum state (twin-beam) may highly increase entanglement.
We present a formulation for investigating quench dynamics across quantum phase transitions in the presence of decoherence. We formulate decoherent dynamics induced by continuous quantum non-demolition measurements of the instantaneous Hamiltonian. We generalize the well-studied universal Kibble-Zurek behavior for linear temporal drive across the critical point. We identify a strong decoherence regime wherein the decoherence time is shorter than the standard correlation time, which varies as the inverse gap above the groundstate. In this regime, we find that the freeze-out time $bar{t}simtau^{{2 u z}/({1+2 u z})}$ for when the system falls out of equilibrium and the associated freeze-out length $bar{xi}simtau^{ u/({1+2 u z})}$ show power-law scaling with respect to the quench rate $1/tau$, where the exponents depend on the correlation length exponent $ u$ and the dynamical exponent $z$ associated with the transition. The universal exponents differ from those of standard Kibble-Zurek scaling. We explicitly demonstrate this scaling behavior in the instance of a topological transition in a Chern insulator system. We show that the freeze-out time scale can be probed from the relaxation of the Hall conductivity. Furthermore, on introducing disorder to break translational invariance, we demonstrate how quenching results in regions of imbalanced excitation density characterized by an emergent length scale which also shows universal scaling. We perform numerical simulations to confirm our analytical predictions and corroborate the scaling arguments that we postulate as universal to a host of systems.
We report some nonsmooth dynamics of a Bloch state in a one-dimensional tight binding model with the periodic boundary condition. After a sudden change of the potential of an arbitrary site, quantities like the survival probability of the particle in the initial Bloch state show cusps periodically, with the period being the Heisenberg time associated with the energy spectrum. This phenomenon is a emph{nonperturbative} counterpart of the nonsmooth dynamics observed previously (Zhang and Haque, arXiv:1404.4280) in a periodically driven tight binding model. Underlying the cusps is an exactly solvable model, which consists of equally spaced levels extending from $-infty$ to $+infty $, between which two arbitrary levels are coupled to each other by the same strength.
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