Diabatic-ramping spectroscopy of many-body excited states

Yoshimura, Bryce; Campbell, W. C.; Freericks, J. K.

doi:10.1103/physreva.90.062334

Cited by 13 publications

(16 citation statements)

References 37 publications

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“…The Our trap has a small 3.4 Hz asymmetry and therefore we expect coupling between motion along e x and e y which becomes more significant at larger effective masses. The sampling times for the measurements shown in equation (4) are small compared to the trap asymmetry and therefore we can locally approximate the motion of the atoms by simple harmonic function with a frequency along e x given by equation (7). Figure A1 illustrates in detail the steps that we take to obtain the dispersion for the periodically driven SOC cases.…”

Section: Resultsmentioning

confidence: 99%

“…We present a Fourier transform technique that employs the connection between the energy spectrum of a system and its dynamics. This connection has been exploited to study the spectrum of both condensed matter [3] and cold atom systems [4,5] alike. We implemented a Fourier transform spectroscopy technique and applied it to spin-orbit coupled (SOC) Bose-Einstein condensates (BECs) to obtain their dispersion relation.…”

Section: Introductionmentioning

confidence: 99%

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Fourier transform spectroscopy of a spin–orbit coupled Bose gas

et al. 2017

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We describe a Fourier transform spectroscopy technique for directly measuring band structures, and apply it to a spin-1 spin–orbit coupled Bose–Einstein condensate. In our technique, we suddenly change the Hamiltonian of the system by adding a spin–orbit coupling interaction and measure populations in different spin states during the subsequent unitary evolution. We then reconstruct the spin and momentum resolved spectrum from the peak frequencies of the Fourier transformed populations. In addition, by periodically modulating the Hamiltonian, we tune the spin–orbit coupling strength and use our spectroscopy technique to probe the resulting dispersion relation. The frequency resolution of our method is limited only by the coherent evolution timescale of the Hamiltonian and can otherwise be applied to any system, for example, to measure the band structure of atoms in optical lattice potentials.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fourier transform spectroscopy of a spin–orbit coupled Bose gas

et al. 2017

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“…Quantum simulation in ion traps has made significant progress over the past five years. Initial work examined the transverse-field Ising model with adiabatic state preparation [1][2][3] and more recently with excited state spectroscopy (since the experiments created significant diabatic excitations) [4][5][6]. The latest work has examined Lieb-Robinson bounds in Ising and XY systems [7,8] and higher-spin variants [9].…”

Section: Introductionmentioning

confidence: 99%

Creating analogs of thermal distributions from diabatic excitations in ion-trap-based quantum simulation

2016

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One broad goal of quantum simulation is to start a simple quantum system in its ground state and slowly evolve the Hamiltonian to a complex one, maintaining the ground state throughout the evolution (called adiabatic state preparation). This provides a natural setting to create a highly entangled and correlated quantum state if the final Hamiltonian supports such a ground state. In iontrap-based quantum simulations, coherence times are too short to allow for such ground-state evolution for large chains, because the rapid evolution of the system creates excitations to higher energy states. Because the probability for this excitation depends exponentially on the excitation energy and because the thermal distribution also depends exponentially on the excitation energy, we investigate whether this so-called diabatic excitation can create the analog of a thermal distribution; as this could serve as an alternative for creating thermal states of complex quantum systems without requiring contact with a heat bath. In this work, we explore this relationship and determine situations, where diabatic excitation can approximately create thermal states.

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“…The downward drift in energies near B 0 = 0 can be attributed to drifts in laser and trap parameters as the experiments progressed from higher to lower fields. An alternative protocol, which follows the time evolution after a quench, has recently been proposed for measuring the critical gap and may scale better for larger systems [32].…”

Section: Measuring a Critical Gapmentioning

confidence: 99%

Coherent imaging spectroscopy of a quantum many-body spin system

Senko

Smith

Richerme

et al. 2014

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Quantum simulators, in which well controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics that is inaccessible to modeling with classical computers. However, checking the results of such simulations will also become classically intractable as system sizes increase. In this work, we introduce and implement a coherent imaging spectroscopic technique to validate a quantum simulation, much as magnetic resonance imaging exposes structure in condensed matter. We use this method to determine the energy levels and interaction strengths of a fully-connected quantum many-body system. Additionally, we directly measure the size of the critical energy gap near a quantum phase transition. We expect this general technique to become an important verification tool for quantum simulators once experiments advance beyond proof-of-principle demonstrations and exceed the resources of conventional computers.Certain classes of quantum many-body systems, which describe a variety of interesting problems including high-T c superconductors or spin liquids, are believed to be fundamentally inaccessible to classical modeling [1]. For example, an interacting spin system following the Ising model can map to NP-complete computational problems [2] and has been applied to understanding neural networks [3] and social behavior [4], yet quickly becomes theoretically intractable due to the exponential number of possible spin configurations [5,6].Quantum simulations [7][8][9][10], in which well-controlled quantum objects like photons [11] or ultracold atoms [12,13] are induced to emulate other quantum systems, are a promising alternative for accessing such problems. However, as these systems approach theoretically intractable physics, validating quantum simulation results will become a major challenge [1,14]. Here we introduce a technique for performing coherent imaging spectroscopy on the Hamiltonian of an interacting many-body spin system. We use spectroscopic imaging to infer spinspin interaction strengths and directly measure the critical energy gap near a quantum phase transition. This technique is a promising benchmarking tool for systems of 30+ spins, where classical computation begins to fail.Ultracold atomic systems are particularly well-suited for simulating interacting spin systems, with the ability to prepare known input states, engineer tunable interaction patterns, and measure individual particles [12,13]. Our experiment uses trapped ions to simulate chains of spin-1/2 particles subject to effective magnetic fields and long-range, inhomogenous Ising couplings generated by optical dipole forces [15][16][17][18][19][20][21][22][23]. This results in an effective N -spin Hamiltonian (with h = 1)where σ γ i (γ = x, y, z) is the Pauli matrix for spin i along direction γ; J i,j ∼ J 0 |i − j| −α is a long-range coupling strength between spins i and j with α tunable between 0 and 3 [15]; and B(t) is the strength of a time-dependent transverse magnetic field.The ability to genera...

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Diabatic-ramping spectroscopy of many-body excited states

Cited by 13 publications

References 37 publications

Fourier transform spectroscopy of a spin–orbit coupled Bose gas

Fourier transform spectroscopy of a spin–orbit coupled Bose gas

Creating analogs of thermal distributions from diabatic excitations in ion-trap-based quantum simulation

Coherent imaging spectroscopy of a quantum many-body spin system

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