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Physical Review Applied

Dissipative Preparation of Generalized Bell States with the Sørensen-Mølmer Setting

P. Z. Zhao, Z. Jin, D. M. Tong

Published Jul 21, 2022• 3 citations
Publisher

Abstract

Quantum entanglement is an important resource in quantum information processing tasks, such as quantum cryptography, quantum teleportation, and quantum computation. The main obstacle to faithful and reliable preparation of entangled states is environment-induced decoherence. Dissipative transition of a general quantum state to an entangled steady state provides an effective strategy to protect entanglement from decoherence, where the decoherence converts into an essential resource. In this paper, we put forward a scheme to prepare generalized Bell states based on trapped ions, in which unitary dynamics and spontaneous emission are combined to drive an arbitrary quantum state in the ground-state space to a unique steady state. The scheme is realized by using the renowned S\o{}rensen-M\o{}lmer setting and is therefore compatible with current experimental technology. Moreover, the vibrational degree of freedom is decoupled from the unitary dynamics so that the scheme does not need to cool the collective vibrational mode to its ground state and thus it works for thermally excited states. Besides, our scheme is demonstrated to be insensitive to variations of some parameters with the aid of numerical simulation.

DOI
10.1103/physrevapplied.18.014051

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Quantum entanglement is an important resource in quantum information processing tasks, such as quantum cryptography, quantum teleportation, and quantum computation. The main obstacle to faithful and reliable preparation of entangled states is environment-induced decoherence. Dissipative transition of a general quantum state to an entangled steady state provides an effective strategy to protect entanglement from decoherence, where the decoherence converts into an essential resource. In this paper, we put forward a scheme to prepare generalized Bell states based on trapped ions, in which unitary dynamics and spontaneous emission are combined to drive an arbitrary quantum state in the ground-state space to a unique steady state. The scheme is realized by using the renowned S\o{}rensen-M\o{}lmer setting and is therefore compatible with current experimental technology. Moreover, the vibrational degree of freedom is decoupled from the unitary dynamics so that the scheme does not need to cool the collective vibrational mode to its ground state and thus it works for thermally excited states. Besides, our scheme is demonstrated to be insensitive to variations of some parameters with the aid of numerical simulation.
We propose a dissipative method for preparation of a maximally entangled steady state of two trapped ions in the Lamb-Dicke limit. By addressing the trapped-ion system with a monochromatic standing-wave laser pulse of frequency resonant with the ionic transition and a microwave field coupled to the ground-state transitions, we obtain an effective coupling between two particles, which is independent of the phonon-number fluctuations. Meanwhile, the controlled spontaneous emission of trapped ions is implemented via pumping the metastable states upwards to the short-lived ionic states by an auxiliary laser field. Combining the unitary processes with the engineered dissipation, a deterministic Bell state can be produced irrespective of the initial states of systems. Moreover, our result shows that the Clauser-Horne-Shimony-Holt inequality can be violated for a wide range of decoherence parameters, even at finite temperature.
Entangled states are a key resource in fundamental quantum physics, quantum cryptography, and quantum computation. In this thesis, we focus on the demonstrations of two novel methods to generate entanglement. First, we implement dissipative production of a maximally entangled steady state on two trapped ions. Dissipative and coherent processes are combined and implemented in a continuous time-independent fashion, analogous to optical pumping of atomic states, continuously driving the system towards the steady entangled state. With this method, we obtain a Bell state fidelity up to 0.89(2). Second, we propose and demonstrate a novel coherent process to confine quantum evolution in a subspace between an initial separable state and the target entangled state. We demonstrate this scheme on two and three ions obtaining a Bell state fidelity up to 0.992(2). Both of these methods are robust against certain types of experimental noise and decoherence. Additionally, we demonstrate sympathetic cooling of ion chains to near the ground\nstate of motion with an electromagnetically-induced-transparency (EIT) method. This results in roughly an order of magnitude faster cooling time while using significantly lower laser power compared to the conventional resolved sideband cooling method. These techniques may be helpful for scaled-up quantum computing.
We propose a nonlocal scheme for preparing a distributed steady-state entanglement of two atoms trapped in separate optical cavities coupled through an optical fiber based on the combined effect of the unitary dynamics and dissipative process. In this scheme, only the qubit of one node is driven by an external classical field, while the other one does not need to be manipulated by an external field. This is meaningful for long distance quantum information processing tasks, and the experimental implementation is greatly simplified due to the unilateral manipulation on one node and the process of entanglement distribution can be avoided. This guarantees the absolute security of long distance quantum information processing tasks and makes the scheme more robust than that based on the unitary dynamics. We introduce the purity to characterize the mixture degree of the target steady-state. The steady entanglement can be obtained independent of the initial state. Furthermore, based on the dissipative entanglement preparation scheme, we construct a quantum teleportation setup with multiple nodes as a practical application, and the numerical simulation demonstrates the scheme can be realized effectively under the current experimental conditions..
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.
This thesis describes schemes for both a fast two-qubit gate operation and the steady-state preparation of a Bell state with trapped ions. A critical figure of merit for quantum computing with trapped ions is the gate duration relative to the decoherence timescale. We propose a fast gate scheme that off ers improvements in time, fidelity and simplicity of implementation over existing fast gate proposals. Our scheme can operate on both neighbouring and non-neighbouring ions in a long ion crystal. This provides a simpler and faster mechanism than traditional gates for complex quantum computing operations on large numbers of ions. The scheme achieves fidelities well above quantum error correction thresholds around 0.0001, and operates arbitrarily fast given arbitrary laser repetition rates. The production of these ultra-fast pulses is an experimental challenge, and fast gates have not yet been implemented; we present an implementation scheme using pulse splitting to provide a higher repetition rate and the pulse timing freedoms required for the gate scheme. We also analyse the effects of errors in the pulses on the gate operation. We analyse another strategy to generate entanglement using a driven dissipative process. Typically, environmental couplings cause decoherence. However, by combining dissipative dynamics with suitably chosen Hamiltonian evolution, the system can be steered to the desired steady states. Our steady-state scheme prepares a maximally-entangled Bell state with fidelity above 0.99, much higher than for schemes implemented with trapped ions. The driven dissipation continuously pumps the system towards the antisymmetric Bell steady-state, which is dark to the system dynamics and robust to parameter variations. The dominant loss mechanism is anomalous heating of the motional modes, reducing our fidelity by less than 0.01 for current experimental rates. Our scheme jointly addresses the ions and does not use sympathetic cooling. We enhance our scheme by combining the dissipative state preparation with the detection of photons, and obtain a significant fidelity enhancement.
Summary form only given. Quantum entanglement is a fundamental element of schemes for quantum communication, cryptography, and computation. In a previous experiment, we demonstrated that two-particle entanglement could be generated in a deterministic way using trapped ions. However, that scheme also could not easily be applied to more particles in a single trap, because it relied on the particular behavior of two ions in a quadrupole RF trap. We have now demonstrated a truly scalable entanglement technique. The scheme is that of a recent proposal by Molmer and Sorensen. Twog /sup 9/Be/sub +/ ions are confined in a linear RF trap, and laser-cooled to near their motional ground state. Lasers are then used to drive Raman transitions between two ground-state hyperfine levels, which are separated by energy hw/sub o/.