Demonstration of a Dressed-State Phase Gate for Trapped Ions

Tan, Ting Rei; Gaebler, John; Bowler, Ryan; Lin, Yiheng; Jost, John D.; Leibfried, D.; Wineland, David J.

doi:10.1103/physrevlett.110.263002

Cited by 63 publications

(84 citation statements)

References 36 publications

(63 reference statements)

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“…By modification of the unitaries [23, 35], it is possible to recover any retarded spin correlation σ α i (t f )σ β j (t 0 ) . We remark that the operations required in each step are performed individually with accuracies better than 99% in current experiments [25].Conclusions.-We have derived a new LRB for a collection of models (1) involving spins and bosons in a lattice. Although the LRB applies to a variety of quantum-optical setups (e.g.…”

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confidence: 85%

“…For this reason, experiments use smaller detunings [5], leading to stronger couplings at the expense of becoming truly long-ranged where the paradigm of LRBs no longer applies [13]. Yet, one can still expect correlation propagation in timescales ∼ 1 ms from the effective model, which are still much slower than the optimal LRB (10) [31].Probing the LRB through fluorescence.-We discuss how to exploit the control and measurement tools of trappedion experiments [25] Figure 2. Experimental sequence to test the LRB: (a) Alwayson and (b) pulsed spin-phonon forces.…”

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confidence: 99%

“…We represent the initialization step in blue, which consists of laser cooling followed by optical pumping P and leads to |↓ · · · ↓ ↓ · · · ↓| ⊗ ρ th , where ρ th is a thermal state of the phonons after Doppler cooling. We then apply a π/2-pulse U j = exp{i π 2 σ y j } by driving the carrier transition [25]. In the measurement step in red, one collects the state-dependent fluorescence M during a continuous driving of the cycling transition [25].…”

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confidence: 99%

“…In particular we show below that the case of trapped ions, a prominent architecture for quantum information [25], is an ideal setup to experimentally test our LRB.…”

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confidence: 99%

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Lieb-Robinson Bounds for Spin-Boson Lattice Models and Trapped Ions

et al. 2013

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We derive a Lieb-Robinson bound for the propagation of spin correlations in a model of spins interacting through a bosonic lattice field, which satisfies itself a Lieb-Robinson bound in the absence of spin-boson couplings. We apply these bounds to a system of trapped ions, and find that the propagation of spin correlations, as mediated by the phonons of the ion crystal, can be faster than the regimes currently explored in experiments. We propose a scheme to test the bounds by measuring retarded correlation functions via the crystal fluorescence.PACS numbers: 03.65. Ud, 03.67.Ac, 37.10.Ty, 03.67.Mn The possibility of designing or simulating many-body systems in quantum-optical setups, such as ultracold atoms [1][2][3][4] or large ion crystals [5], is stimulating considerable progress in our understanding of non-equilibrium quantum many-body phenomena. However, the interpretation of these experiments demands powerful theoretical tools, including the LiebRobinson bounds (LRBs) [6] developed in this work. On the surface, LRBs show that non-relativistic quantum many-body systems, under certain conditions, display a causal structure analogous to relativistic quantum field theories. More deeply, LRBs are essential to prove fundamental quantum many-body properties, such as the exponential decay of correlations in the ground-state of gapped local Hamiltonians -the so-called "clustering of correlations" [7]-, scaling laws for entanglement entropy [8] -the "area laws" [9] -, or the robustness of topological order under local perturbations [10].Causality limits how local measurements and perturbations, described by an operator O X in region X, affect later measurements of another operator O Y in a separate region Y [11]. In analogy to Heisenberg's principle [12], this uncertainty is quantified by a commutator C Y,X (t) = [O Y (t), O X (0)] . Lorentz invariance and the mathematical structure of relativistic theories guarantee causality [11]. Thus, C Y,X (t) = 0 when the distance d XY > ct places both regions outside the light cone defined by the speed of light c. In non-relativistic quantum mechanics, causality is violated at the few particle level [11]. Remarkably, in the many-body regime, an approximate light cone emerges, outside of which such correlations are vanishingly small. This phenomenon, first demonstrated by Lieb and Robinson [6] for a lattice of locally-interacting spins, has been generalized to finite-dimensional models, anharmonic oscillators and master equations [7,[13][14][15][16].In this work, we address the role of bosons as mediators of interactions between particles in the light of LRBs. This is done for a general model of finite dimensional systems interacting through a bosonic field that satisfies a LRB itself. New bounds are derived, which are then applied to a crystal of trapped atomic ions, where the spins and the bosons map to the ions' internal states and the crystal's phonons, respectively. These LRBs work for all spin-boson lattice models of any dimensionality and geometry realized with sta...

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confidence: 85%

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confidence: 99%

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confidence: 99%

“…In particular we show below that the case of trapped ions, a prominent architecture for quantum information [25], is an ideal setup to experimentally test our LRB.…”

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confidence: 99%

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Lieb-Robinson Bounds for Spin-Boson Lattice Models and Trapped Ions

et al. 2013

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“…These electrically charged particles are confined in an electromagnetic trap, micrometers apart from one another [4,5]. Thanks to precise spin manipulation capabilities, near-perfect spin readout, and a variety of cooling [6,7] and dynamical decoupling techniques [8][9][10][11][12][13][14][15][16], trapped ions can be made to follow target Hamiltonians with high fidelity [17,18], making them one of the most promising candidates for quantum simulation.…”

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confidence: 99%

Simulating the Haldane phase in trapped-ion spins using optical fields

et al. 2015

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We propose to experimentally explore the Haldane phase in spin-one XXZ antiferromagnetic chains using trapped ions. We show how to adiabatically prepare the ground states of the Haldane phase, demonstrate their robustness against sources of experimental noise, and propose ways to detect the Haldane ground states based on their excitation gap and exponentially decaying correlations, nonvanishing nonlocal string order, and doublydegenerate entanglement spectrum.

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Continuous dynamical decoupling utilizing time‐dependent detuning

Cohen

Aharon

Retzker

2016

Fortschritte der Physik

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The coherence times achieved with continuous dynamical decoupling techniques are often limited by fluctuations in the driving amplitude. In this work, we use time-dependent phase-modulated continuous driving to increase the robustness against such fluctuations in a dense ensemble of nitrogen-vacancy centers in diamond. Considering realistic experimental errors in the system, we identify the optimal modulation strength, and demonstrate an improvement of an order of magnitude in the spin-preservation of arbitrary states over conventional single continuous driving. The phase-modulated driving exhibits comparable results to previously examined amplitude-modulated techniques, and is expected to outperform them in experimental systems having higher phase accuracy. The proposed technique could open new avenues for quantum information processing and many body physics, in systems dominated by high-frequency spin-bath noise, for which pulsed dynamical decoupling is less effective. PACS numbers: 76.30.Mi One of the main challenges in quantum information processing, quantum computing and quantum sensing is the preservation of arbitrary spin states. For example, the sensitivity of nitrogen-vacancy (NV) ensemble-based AC magneteometry scales as a square-root of the coherence time [1-8]. Moreover, long ensemble spin coherence times could open new avenues for studying many body dynamics of interacting spins [9-11]. The commonly used technique for improving coherence times and preserving arbitrary states is dynamical decoupling (DD) sequences [12-18]. Although pulsed DD is very efficient for a variety of physical systems, continuous driving-based decoupling (i.e. spin-lock) has an advantage when the power spectrum of the noise bath contains a significant contribution from high-frequency terms, such that relevant correlation times are shorter than the duty cycle achievable by pulsed techniques [15, 16]. However, in these continuous schemes, amplitude fluctuations of the driving source itself limit the achieved coherence times, raising the need for a fault tolerant driving [16, 18-23]. One common approach for overcoming fluctuations in the driving amplitude is to flip the phase of the continuous driving every time increment τ (i.e., to apply a "rotary echo", [24]). However, in the basis of the dressed states, these techniques are equivalent to pulsed DD, having the same disadvantages, such as additional imperfections due to the application of non-ideal pulses, and the disability of mitigating amplitude fluctuations that are faster than the flipping rate 1/τ. Another approach for overcoming these fluctuations is to apply an additional continuous driving in the perpendicular axis [Fig. 1(a)]. In order to avoid the use of an extra microwave (MW) source, the same effective Hamiltonian can be generated by a time-dependent modulation of the amplitude or phase of the original driving. Recently, such time-dependent amplitude modulation was experimentally demonstrated in a system of single isolated NV centers, achieving an order of magnitu...

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Demonstration of a Dressed-State Phase Gate for Trapped Ions

Cited by 63 publications

References 36 publications

Lieb-Robinson Bounds for Spin-Boson Lattice Models and Trapped Ions

Lieb-Robinson Bounds for Spin-Boson Lattice Models and Trapped Ions

Simulating the Haldane phase in trapped-ion spins using optical fields

Continuous dynamical decoupling utilizing time‐dependent detuning

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