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arXiv:1709.00472 · Physical Review A

Steady many-body entanglements in dissipative systems

G. D. de Moraes Neto, Victor Fernandes Teizen, Víctor Montenegro, E. Vernek

Published Dec 13, 2017• 14 citations
arXivHTMLPDF

Abstract

We propose a dissipative method for the preparation of many-body steady entangled states in spin and fermionic chains. The scheme is accomplished by means of an engineered set of Lindbladians acting over the eigenmodes of the system, whose spectrum is assumed to be resolvable. We apply this idea to prepare a particular entangled state of a spin chain described by the $XY$ model, emphasizing its generality and experimental feasibility. Our results show that our proposal is capable of achieving high fidelities and purities for a given target state, even when dephasing and thermal dissipative processes are taken into account. Moreover, the method exhibits a remarkable robustness against fluctuations in the model parameters.

DOI
10.1103/physreva.96.062313

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We propose a dissipative method for the preparation of many-body steady entangled states in spin and fermionic chains. The scheme is accomplished by means of an engineered set of Lindbladians acting over the eigenmodes of the system, whose spectrum is assumed to be resolvable. We apply this idea to prepare a particular entangled state of a spin chain described by the XYXYXY model, emphasizing its generality and experimental feasibility. Our results show that our proposal is capable of achieving high fidelities and purities for a given target state, even when dephasing and thermal dissipative processes are taken into account. Moreover, the method exhibits a remarkable robustness against fluctuations in the model parameters.
Abstract We present a scheme for the dissipative preparation of an entangled steady state between two atomic qubits separately trapped in the coupled cavities. The combination of coherent driving fields and dissipative processes will drive the system into a steady state. By choosing different frequency of classical laser field, the target steady state can be generated in different ways. In our scheme, the atomic spontaneous emission and the cavity decay can be used as a prerequisite. The numerical simulation shows that the maximally entangled state with high fidelity and purity can be produced regardless of the initial state. The fidelity is insensitive to the fluctuation of the system parameters.
The controlled preparation of quantum many-body states is a central challenge for quantum technologies. While preparing target states coherently is possible in principle, it is often fragile and experimentally demanding. Dissipative state preparation, where engineered environments drive the system toward desired steady states, provides a complementary and powerful paradigm. This thesis explores dissipative methods for preparing complex many-body states along three distinct directions. First, we investigate the dissipative stabilization of injective matrix product states (MPS). Injective MPS are particularly well suited for dissipative preparation because they arise as ground states of frustration-free parent Hamiltonians, allowing for tailored jump operators to steer the system directly into the target state. We showcase the surprising result that such state preparation works even in the dilute limit where steering only acts on a single link. Moreover, we introduce a formalism for engineering additional coherent interactions, extending the set of accessible states. Second, and complementary to steering, we develop and analyze a universal cooling scheme capable of preparing ground states even in frustrated quantum systems. In contrast to steering methods, universal cooling can overcome the glass floor that forbids steering methods to prepare such frustrated ground states. A key insight here is that the presented cooling scheme is completely system-agnostic making it extremely robust. Finally, we pursue dressing of the system eigenstates by means of either classical drives or coherent interactions as a means to influence the action of dissipation on the system. Focusing first on time-dependent systems, we propose a generalized numerical implementation of non-adiabatic master equations suitable for the use of optimal control tools. Additionally, we investigate how the collective coupling between a spin ensemble and a cavity can steer the system into a spin-squeezed steady state. Together, these three avenues illustrate how tailored dissipative dynamics can extend the frontier of many-body state preparation, from stabilizing injective MPS to cooling complex frustrated systems and generating non-classical steady states in the dressed framework.
We present a scheme for the dissipative preparation of an entangled steady state of two superconducting qubits in a circuit quantum electrodynamics (QED) setup. Combining resonator photon loss---a dissipative process already present in the setup---with an effective two-photon microwave drive, we engineer an effective decay mechanism which prepares a maximally entangled state of the two qubits. This state is then maintained as the steady state of the driven, dissipative evolution. The performance of the dissipative state preparation protocol is studied analytically and verified numerically. In view of the experimental implementation of the presented scheme we investigate the effects of potential experimental imperfections and show that our scheme is robust to small deviations in the parameters. We find that high fidelities with the target state can be achieved both with state-of-the-art three-dimensional, as well as with the more commonly used two-dimensional transmons. The promising results of our study thus open a route for the demonstration of a highly entangled steady state in circuit QED.
We present a technique for the dissipative preparation of highly entangled multiparticle states of atoms coupled to common oscillator modes. By combining local spontaneous emission with coherent couplings, we engineer many-body dissipation that drives the system from an arbitrary initial state into a Greenberger-Horne-Zeilinger state. We demonstrate that using our technique highly entangled steady states can be prepared efficiently in a time that scales polynomially with the system size. Our protocol assumes generic couplings and will thus enable the dissipative production of multiparticle entanglement in a wide range of physical systems. As an example, we demonstrate the feasibility of our scheme in state-of-the-art trapped-ion systems.
Abstract Preparation of entangled steady states via dissipation and pumping in Rydberg atoms has been recently found to be useful for quantum information processing. The driven-dissipative dynamics is closely related to the natural linewidth of the Rydberg states and can be usually modulated by engineering the thermal reservior. Instead of modifying the effectively radiative decay, we propose an alternatively optimized scheme, which combines the resonant Rydberg antiblockade excitation and the Lyapunov control of the ground states to speed up the prepration of the singlet state for two interacting Rydberg atoms. The acceleration process strongly depends on the initial state of the system with respect to the initial coherence between the singlet state and decoherence-sensitive bright state. We study the optimal parameter regime for fast entanglement preparation and the robustness of the fidelity against random noises. The numerical results show that a fidelity above 0.99 can be achieved around 0.4 ms with the current experimental parameters. The scheme may be generalized for preparation of more complicate multi-atom entangled states.
We propose a dissipative method to prepare the ground state of the isotropic XY spin Hamiltonian in a transverse field. Our model consists of a spin chain with nearest-neighbor interactions and an additional collective coupling of the spins to a damped harmonic oscillator. The latter provides an effective environment with a Lorentzian spectral density and can be used to drive the chain asymptotically toward its multipartite-entangled ground state at a rate that depends on the degree of non-Markovianity of the evolution. We also present a detailed proposal for the experimental implementation with a chain of trapped ions. The protocol does not require individual addressing, concatenated pulses, or multi-particle jump operators, and is capable of generating the desired target state in small ion chains with very high fidelities.