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

Cohen, Itsik; Richerme, Philip; Gong, Zhe-Xuan; Monroe, C.; Retzker, Alex

doi:10.1103/physreva.92.012334

Cited by 29 publications

(34 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Additional numerical calculations are needed to accurately determine the central charge at the CSB-Haldane-AFM tricritical point. Generalizations of our model to include single-ion anisotropy and a magnetic field are readily achievable in current trapped-ion experiments 55,56 . Understanding these exotic quantum phase transitions-induced by long-range interactions that are highly tunable in current experiments-requires the confrontation of numerous theoretical and numerical challenges, and motivates experimental quantum simulation of the model using AMO systems.…”

Section: Discussionmentioning

confidence: 99%

“…The simulation of Eq. (1) are suppressed 55,56 . Finally, we point out that, even in the experimental setup already demonstrated in Ref.…”

Section: Experimental Detectionmentioning

confidence: 99%

“…54,55 that the Hamiltonian we consider can be simulated (for widely tunable J z and 0 < α < 3) by using microwave field gradients or optical dipole forces to induce spin-spin interactions in a chain of trapped ions. The simulation of Eq.…”

Section: Experimental Detectionmentioning

confidence: 99%

“…Our study is largely motivated by imminent trapped-ion based experiments that can simulate this model with widely tunable index α [54][55][56] . In the absence of long-range interactions, the choice of spin-1 over spin-1/2 allows us to have four distinct quantum phases by varying the anisotropy of the interactions: a ferromagnetic (FM) phase and an antiferromagnetic (AFM) Ising phase that are both gapped and long-range ordered, a disordered gapless phase (the XY phase), and a gapped and topologically ordered phase (the Haldane phase).…”

mentioning

confidence: 99%

See 3 more Smart Citations

Kaleidoscope of quantum phases in a long-range interacting spin-1 chain

Gong

Maghrebi

et al. 2016

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

Motivated by recent trapped-ion quantum simulation experiments, we carry out a comprehensive study of the phase diagram of a spin-1 chain with XXZ-type interactions that decay as $1/r^{\alpha}$, using a combination of finite and infinite-size DMRG calculations, spin-wave analysis, and field theory. In the absence of long-range interactions, varying the spin-coupling anisotropy leads to four distinct phases: a ferromagnetic Ising phase, a disordered XY phase, a topological Haldane phase, and an antiferromagnetic Ising phase. If long-range interactions are antiferromagnetic and thus frustrated, we find primarily a quantitative change of the phase boundaries. On the other hand, ferromagnetic (non-frustrated) long-range interactions qualitatively impact the entire phase diagram. Importantly, for $\alpha\lesssim3$, long-range interactions destroy the Haldane phase, break the conformal symmetry of the XY phase, give rise to a new phase that spontaneously breaks a $U(1)$ continuous symmetry, and introduce an exotic tricritical point with no direct parallel in short-range interacting spin chains. We show that the main signatures of all five phases found could be observed experimentally in the near future.Comment: 11 pages, 6 figure

show abstract

Section: Discussionmentioning

confidence: 99%

“…The simulation of Eq. (1) are suppressed 55,56 . Finally, we point out that, even in the experimental setup already demonstrated in Ref.…”

Section: Experimental Detectionmentioning

confidence: 99%

Section: Experimental Detectionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Kaleidoscope of quantum phases in a long-range interacting spin-1 chain

Gong

Maghrebi

et al. 2016

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Continuous dynamical decoupling utilizing time‐dependent detuning

Cohen

Aharon

Retzker

2016

Fortschritte der Physik

Self Cite

View full text Add to dashboard Cite

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...

show abstract

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

Cited by 29 publications

References 60 publications

Kaleidoscope of quantum phases in a long-range interacting spin-1 chain

Kaleidoscope of quantum phases in a long-range interacting spin-1 chain

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

Continuous dynamical decoupling utilizing time‐dependent detuning

Contact Info

Product

Resources

About