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arXiv:1603.03848 · Physical Review Letters

Preparation of Entangled States through Hilbert Space Engineering

Yiheng Lin, John Gaebler, Florentin Reiter, Ting Rei Tan, R. Bowler, Y. Wan, Adam C. Keith, Emanuel H. Knill, Scott Glancy, Kevin J. Coakley, Anders Søndberg Sørensen, Dietrich G. Leibfried, David J. Wineland

Published Sep 28, 2016• 41 citations
arXivHTMLPDF

Abstract

We apply laser fields to trapped atomic ions to constrain the quantum dynamics from a simultaneously applied global microwave field to an initial product state and a target entangled state. This approach comes under what has become known in the literature as "quantum Zeno dynamics" and we use it to prepare entangled states of two and three ions. With two trapped ^{9}Be^{+} ions, we obtain Bell state fidelities up to 0.990_{-5}^{+2}; with three ions, a W-state fidelity of 0.910_{-7}^{+4} is obtained. Compared to other methods of producing entanglement in trapped ions, this procedure can be relatively insensitive to certain imperfections such as fluctuations in laser intensity.

DOI
10.1103/physrevlett.117.140502

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We apply laser fields to trapped atomic ions to constrain the quantum dynamics from a simultaneously applied global microwave field to an initial product state and a target entangled state. This approach comes under what has become known in the literature as "quantum Zeno dynamics" and we use it to prepare entangled states of two and three ions. With two trapped ^{9}Be^{+} ions, we obtain Bell state fidelities up to 0.990_{-5}^{+2}; with three ions, a W-state fidelity of 0.910_{-7}^{+4} is obtained. Compared to other methods of producing entanglement in trapped ions, this procedure can be relatively insensitive to certain imperfections such as fluctuations in laser intensity.
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.
A new mechanism is proposed for dissipatively preparing maximal Bell entangled state of two atoms in an optical cavity. This scheme integrates the spontaneous emission, the light shift of atoms in the presence of dispersive microwave field, and the quantum Zeno dynamics induced by continuous coupling, to obtain a unique steady state irrespective of initial state. Even for a large cavity decay, a high-fidelity entangled state is achievable at a short convergence time, since the occupation of the cavity mode is inhibited by the Zeno requirement. Therefore, a low single-atom cooperativity C=g2/(κγ) is good enough for realizing a high fidelity of entanglement in a wide range of decoherence parameters. As a straightforward extension, the feasibility for preparation of two-atom Knill–Laflamme–Milburn state with the same mechanism is also discussed.
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.
Three experimentally feasible schemes are proposed for generating multipartite entangled states of cold trapped ions.In the first scheme,a GHZ state can be simply synthesized in a single step. The second scheme is to prepare fully symmetric W states with two steps.The third scheme describes the sequential generation of linear cluster states.In addition,a method to create a larger cluster state was also presented by fuzing the end qubits of two smaller cluster states in order to decrease the distortion caused by decoherence,which can speed up the generation of large cluster states.The above schemes involve the collective interaction between multiple ions with the vibrational ground state and a large detuned laser. Compared with previous schemes,the above schemes have four advantages.Firstly,they do not require the vibrational mode of ions as memory.Secondly,they do not need to address the ions individually.Thirdly, they are free from the effects of phase fluctuation of laser field.Finally,they need less operations.
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.
A robust scheme is proposed for producing maximally entangled states for many trapped ions in thermal motion. In the scheme the ions are simultaneously illuminated by two standing-wave laser fields. During the operation the phases of the lasers are inverted, which not only cancels the vibration-dependent parts in the evolution operator, but also suppresses direct off-resonant coupling of the internal states. Thus, our scheme allows the production of entanglement for hot trapped ions with laser fields of high intensity, which makes the entanglement speed extremely high.