Proposal for Verification of the Haldane Phase Using Trapped Ions

Cohen, Itsik; Retzker, Alex

doi:10.1103/physrevlett.112.040503

Cited by 39 publications

(57 citation statements)

References 65 publications

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“…Experimentally, the following parameters are realistic: ν n = 2π · 5MHz, δ = 2π · 5.1MHz, Ω = 2π · 500kHz,η n, j ≈ 0.14, Ω = 2π · 10kHz, which gives J e f f i,i+1 ≈ 2π · 1kHz, such that 0 < D < 2π · 10kHz. An important advantage over the previous derivation in [40], is that in order to obtain the antiferromagnetic interactions, δ should be larger than the secular frequencies of the radial vibrational modes, rather than the Rabi frequency Ω/ √ 2. Since one of the main experimental challenges is to reach a high Rabi frequency, in the present derivation we overcome this technical obstacle.…”

Section: Modelmentioning

confidence: 99%

“…In the above scheme, the Ising-like λ parameter is limited 0 ≤ λ ≤ 2, and we can not cover the whole phase diagram, just like in the derivation of the previous paper [40]. This has to do with the F i β F j β term, where α ⊥ β , in the XX Hamiltonian (eq.3).…”

Section: Verification Of the Haldane Phase's Ground Statementioning

confidence: 99%

“…By enlarging the spin's degree and moving into integer spin chains, new and subtle physics can appear [33][34][35][36][37][38][39][40][41]; for example, the local orders vanish and we are left with hidden orders only [42].…”

Section: Introductionmentioning

confidence: 99%

“…Previously, we proposed how to engineer the Hamiltonian of Eq. 1 using microwave-based forces on the trapped ion spins [40]. In this previous derivation of the Hamiltonian, we could cover only 0 ≤ λ ≤ 2 of the phase diagram ( Fig.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Modelmentioning

confidence: 99%

Section: Verification Of the Haldane Phase's Ground Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2015

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“…The comparison of the properties of integer * corresponding author; e-mail: A.Drzewinski@if.uz.zgora.pl and half-integer spin chains may be realized with trapped ultra-cold atomic gases [7]. It opens the experimental way to investigate the dynamical properties of the Haldane state [8,9] and gives the motivation for our theoretical research.…”

Section: Introductionmentioning

confidence: 99%

Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy

2016

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In the framework of the matrix product state representation the effect of a sudden turning on of the uniaxial anisotropy on the time evolution of the Haldane state has been investigated. Depending on the value of the uniaxial anisotropy parameter, the calculations were derived within (or outside) the region where the Haldane gap survives. An exact expression for the time evolution of the Loschmidt echo has been derived and, moreover, its collapse and revival behaviour was captured. In addition, the non-local order parameter of a time evolving state was tracked, revealing two types of relaxations.

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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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Proposal for Verification of the Haldane Phase Using Trapped Ions

Cited by 39 publications

References 65 publications

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

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

Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy

Continuous dynamical decoupling utilizing time‐dependent detuning

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