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Optics Express

Inverse incoherent engineering

Wei Ma, Xiaojun Cao, S. L. Wu

Published Sep 19, 2017• 3 citations
Publisher

Abstract

We propose a protocol to construct shortcuts of adiabaticity for open quantum systems in unitary evolution. Using the dynamical invariants of open quantum systems, we design a convenient form of the driver Hamiltonian to accelerate the adiabatic decoherence free subspaces scheme (TDFs) and engineer a quantum state from the initial state into the target state. Since the trajectory of TDFSs is determined by the incoherent control process, we would like to call it as the inverse incoherent engineering protocol. We apply the method to a two-qubits system which interacts with a time-dependent vacuum squeezed field to prepare some maximally entangled states of it. The results illustrate that our protocol can be used both in the adiabatic and nonadiabatic regime with perfect fidelity.

DOI
10.1364/oe.25.023850

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We propose a protocol to construct shortcuts of adiabaticity for open quantum systems in unitary evolution. Using the dynamical invariants of open quantum systems, we design a convenient form of the driver Hamiltonian to accelerate the adiabatic decoherence free subspaces scheme (TDFs) and engineer a quantum state from the initial state into the target state. Since the trajectory of TDFSs is determined by the incoherent control process, we would like to call it as the inverse incoherent engineering protocol. We apply the method to a two-qubits system which interacts with a time-dependent vacuum squeezed field to prepare some maximally entangled states of it. The results illustrate that our protocol can be used both in the adiabatic and nonadiabatic regime with perfect fidelity.
The adiabatic theorem and shortcuts to adiabaticity for time-dependent open quantum systems are explored in this paper. Starting from the definition of dynamical stable decoherence-free subspace, we show that, under a compact adiabatic condition, the quantum state remains in the time-dependent decoherence-free subspace with an extremely high purity, even though the dynamics of the open quantum system may not be adiabatic. The adiabatic condition mentioned here in the adiabatic theorem for open systems is very similar to that for closed quantum systems, except that the operators required to change slowly are the Lindblad operators. We also show that the adiabatic evolution of decoherence-free subspaces depends on the existence of instantaneous decoherence-free subspaces, which requires that the Hamiltonian of open quantum systems be engineered according to the incoherent control protocol. In addition, shortcuts to adiabaticity for adiabatic decoherence-free subspaces are also presented based on the transitionless quantum driving method. Finally, we provide an example that consists of a two-level system coupled to a broadband squeezed vacuum field to show our theory. Our approach employs Markovian master equations and the theory can apply to finite-dimensional quantum open systems.
We propose a fast mixed-state control scheme to transfer the quantum state along designable trajectories in Hilbert space, which is robust to multiple decoherence noises. Starting with the dynamical invariants of open quantum systems, we present the shortcuts to adiabaticity (STA) of open quantum systems at first, then apply the STA to speed up the adiabatic steady process. Our scheme drives open systems from a initial steady state to a target steady state by a controlled Liouvillian that possesses the same form as the reference (original) one that is accessible in present-day experiments. An experimental design with currently available parameters for the nitrogen-vacancy (N-VVV) center in diamond is suggested and discussed.
Pure-state inverse engineering among the schemes of shortcuts to adiabaticity is a widespread utility in applications to quantum computation and quantum simulation. While in principle it can realise the fast control of quantum systems with high fidelity, in practice this fast control is severely hindered by infinite energy gaps and impractical control fields. To circumvent this problem, we propose a scheme of shortcuts to adiabaticity of mixed state based on the dynamical invariant of open quantum system. Our scheme can drives a steady state to a target steady state of the open system by a controlled Liouvillian that possesses the same form as the reference (original) one. We apply this scheme to stimulated Raman adiabatic passage (STIRAP) and find that an almost perfect population transfer can be obtained. The experimental observation with currently available parameters for the nitrogen-vacancy (NV) center in diamond is suggested and discussed.
We propose a scheme for inverse engineering control in open quantum systems. Starting from an undetermined time evolution operator, a time-dependent Hamiltonian is derived in order to guide the system to attain an arbitrary target state at a predefined time. We calculate the fidelity of our inverse engineering control protocol in the presence of the noise with respect to the stochastic fluctuation of the linear parameters of the Hamiltonian during the time evolution. For a special family of Hamiltonians for two-level systems, we show that the control evolution of the system under noise can be categorized into two standard decohering processes: dephasing and depolarization, for both Markovian and non-Markovian conditions. In particular, we illustrate our formalism by analyzing the robustness of the engineered target state against errors. Moreover, we discuss the generalization of the inverse protocol for higher-dimensional systems.
Different methods have been recently put forward and implemented experimentally to inverse engineer the time-dependent Hamiltonian of a quantum system and accelerate slow adiabatic processes via nonadiabatic shortcuts. In the ``transitionless quantum driving'' proposed by Berry, shortcut Hamiltonians are designed so that the system follows exactly, in an arbitrarily short time, the approximate adiabatic path defined by a reference Hamiltonian. A different approach is based on first designing a Lewis-Riesenfeld invariant to carry the eigenstates of a Hamiltonian from specified initial to final configurations, again in an arbitrary time, and then constructing from the invariant the transient Hamiltonian that connects these boundary configurations. We show that the two approaches, apparently quite different in form and so far in results, are, in fact, strongly related and potentially equivalent, so that the inverse-engineering operations in one of them can be reinterpreted and understood in terms of the concepts and operations of the other one. We study, as explicit examples, expansions of time-dependent harmonic traps and the state preparation of two-level systems.
The mixed-state inverse engineering scheme is a control scheme used for engineering the quantum state of a driven open quantum system from an initial steady state to a final steady state. In this paper, we present an analytical study of this scheme applied to the driven two-level model coupled to a heat reservoir. Typically, when the purity of the quantum state varies, incoherent control techniques are required for mixed-state engineering. However, we show that for both Markovian and non-Markovian dynamics, coherent control protocols can transfer the quantum state into the target state. This simplification comes at a cost, as the evolution of the quantum state must be limited to restricted conditions, resulting in special trajectories in its Hilbert space that connect the initial and target states.