Beyond the Spin Model Approximation for Ramsey Spectroscopy

Koller, Andrew; Beverland, Michael E.; Gorshkov, Alexey V.; Rey, Ana María

doi:10.1103/physrevlett.112.123001

Cited by 6 publications

(8 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using this formulation, we gain a great deal of insight about the dynamics, and can extract analytic solutions for spin observables and correlations in several limits. Although spin models in energy space [19][20][21][22][23][24][25] have been used before and agreed well with experiments [5,23,[26][27][28][29][30], their use was limited to pure spin dynamics (no motion). Our formulation allows us to track motional degrees of freedom, compute local observables, and determine how correlations spread in real space.…”

mentioning

confidence: 76%

“…However, processes that do conserve single particle energy, but at the same time change the populated single particle modes, i.e. "resonant" mode changes, can be important for a harmonic trap [24]. While there are a large number of such terms in a harmonic trap due to the equal spacing of energy levels, realistic optical traps in cold atom experiments include anharmonicity which breaks these degeneracies.…”

Section: The Generalized Spin Model Approximation: Validity and Discu...mentioning

confidence: 99%

See 1 more Smart Citation

Dynamics of Interacting Fermions in Spin-Dependent Potentials

Koller¹,

Wall²,

Mundinger³

et al. 2016

Phys. Rev. Lett.

View full text Add to dashboard Cite

Recent experiments with dilute trapped Fermi gases observed that weak interactions can drastically modify spin transport dynamics and give rise to robust collective effects including global demagnetization, macroscopic spin waves, spin segregation, and spin self-rephasing. In this work we develop a framework for studying the dynamics of weakly interacting fermionic gases following a spin-dependent change of the trapping potential which illuminates the interplay between spin, motion, Fermi statistics, and interactions. The key idea is the projection of the state of the system onto a set of lattice spin models defined on the single-particle mode space. Collective phenomena, including the global spreading of quantum correlations in real space, arise as a consequence of the long-ranged character of the spin model couplings. This approach achieves good agreement with prior measurements and suggests a number of directions for future experiments.The interplay between spin and motional degrees of freedom in interacting electron systems has been a longstanding research topic in condensed matter physics. Interactions can modify the behavior of individual electrons and give rise to emergent collective phenomena such as superconductivity and colossal magnetoresistance [1]. Theoretical understanding of non-equilibrium dynamics in interacting fermionic matter is limited, however, and many open questions remain. Ultracold atomic Fermi gases, with precisely controllable parameters, offer an outstanding opportunity to investigate the emergence of collective behavior in out-of-equilibrium settings.Progress in this direction has been made in recent experiments with ultracold spin-1/2 fermionic vapors, where initially spin-polarized gases were subjected to a spin-dependent trapping potential ( Fig. 1) implemented by a magnetic field gradient [2-4], or a spin-dependent harmonic trapping frequency [5-8] -equivalent to a spatially-varying gradient. Even in the weakly interacting regime, drastic modifications of the single-particle dynamics were reported. Moreover, despite the local character of the interactions, collective phenomena were observed, including demagnetization and transverse spinwaves in the former, and a time-dependent separation (segregation) of the spin densities and spin self-rephasing in the latter. Although mean-field and kinetic theory formulations have explained some of these phenomena [8][9][10][11][12][13][14][15][16][17][18], a theory capable of describing all the time scales and the interplay between spin, motion, and interactions has not been developed.In this work, we develop a framework that accounts for the coupling of spin and motion in weakly interacting Fermi gases. We qualitatively reproduce and explain all phenomena of the aforementioned experiments and obtain quantitative agreement with the results of Ref. [7]. In this formulation the state of the system is represented as a superposition of spin configurations which live on lattices whose sites correspond to modes of the underlying single-particle sy...

show abstract

mentioning

confidence: 76%

Section: The Generalized Spin Model Approximation: Validity and Discu...mentioning

confidence: 99%

Dynamics of Interacting Fermions in Spin-Dependent Potentials

Koller¹,

Wall²,

Mundinger³

et al. 2016

Phys. Rev. Lett.

View full text Add to dashboard Cite

show abstract

“…The key approximation in our approach, whose validity we investigate in detail, is that the single-particle motional states are not changed by interactions, but interactions can affect spin dynamics though exchange. While this approach is only formally valid in the regime in which the characteristic interaction energy per particle U is weak compared to the trap energy scale ω, many relevant quantities, such as the demagnetization time of a polarized ensemble, can be evaluated with much greater accuracy [15]. If the single-particle mode quantum numbers of the trap are thought of as enumerating positions on a regular spatial array which we call the energy lattice (Fig.…”

Section: Introductionmentioning

confidence: 99%

Simulating fermions in spin-dependent potentials with spin models on an energy lattice

Wall

2020

Preprint

View full text Add to dashboard Cite

We study spin-1/2 fermions in spin dependent potentials under the spin model approximation, in which interatomic collisions that change the total occupation of single-particle modes are ignored. The spin model approximation maps the interacting fermion problem to an ensemble of lattice spin models in energy space, where spin-spin interactions are long-ranged and spin-anisotropic. We show that the spin model approximation is accurate for weak interactions compared to the harmonic oscillator frequency, and captures the collective spin dynamics to timescales much longer than would be expected from perturbation theory. We explore corrections to the spin model, and the relative importance of corrections when realistic anharmonic potential corrections are taken into account. Additionally, we present numerical techniques that are useful for analysis of spin models on an energy lattice, including enacting a change of single-particle basis on a many-body state as an effective time evolution, and fitting of spatially inhomogeneous long-range interactions with exponentials. This latter technique is useful for constructing matrix product operators for use in DMRG analyses, and may have broader applicability within the tensor network community.

show abstract

“…The first crucial ingredient for implementing such a spin model is to depart from second-order superexchange interactions and use contact interactions to first order [23][24][25][26][27][28][29][30][31][32]. As shown in Fig.…”

mentioning

confidence: 99%

“…It is therefore tempting to circumvent the problem of high motional temperature by constructing a spin model in such a way that the motional and spin degrees of freedom are effectively decoupled. We provide a recipe for such a decoupling and hence for realizing spin models with thermal atoms.The first crucial ingredient for implementing such a spin model is to depart from second-order superexchange interactions and use contact interactions to first order [23][24][25][26][27][28][29][30][31][32]. As shown in Fig.…”

mentioning

confidence: 99%

Realizing exactly solvableSU(N)magnets with thermal atoms

et al. 2016

View full text Add to dashboard Cite

We show that n thermal fermionic alkaline-earth-metal atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the S n symmetry that permutes atoms occupying different vibrational levels of the trap and the SU(N ) symmetry associated with N nuclear spin states. The symmetries make the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU(N ) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary nonthermal distribution.DOI: 10.1103/PhysRevA.93.051601The study of quantum spin models with ultracold atoms [1,2] promises to give crucial insights into a range of equilibrium and nonequilibrium many-body phenomena from quantum spin liquids [3] and many-body localization [4] to quantum quenches [5][6][7] and quantum annealing [8]. While other approaches exist [9][10][11][12], the most common approach taken to implement a quantum spin model with ultracold atoms relies on preparing a Mott insulator in an optical lattice, where the internal states of atoms on each site define the effective spin [1,[13][14][15][16][17][18][19]. Virtual hopping processes to neighboring sites and back then give rise to effective superexchange spin-spin interactions. Since the superexchange interactions are typically very weak ( kHz) [1] (unless the traps are operated near surfaces, which can reduce spacings and increase energy scales [20][21][22]), it is a significant challenge in experimental cold-atom physics to achieve temperatures and decoherence rates low enough to access superexchange-based quantum magnetism.Since ultracold atoms can be prepared in specific internal (i.e., spin) states with extremely high precision, spin temperatures that can be realized are much lower than the experimentally achievable motional temperatures. It is therefore tempting to circumvent the problem of high motional temperature by constructing a spin model in such a way that the motional and spin degrees of freedom are effectively decoupled. We provide a recipe for such a decoupling and hence for realizing spin models with thermal atoms.The first crucial ingredient for implementing such a spin model is to depart from second-order superexchange interactions and use contact interactions to first order [23][24][25][26][27][28][29][30][31][32]. As shown in Fig. 1(a), this can be achieved if all atoms sit in different orbitals of the same anharmonic trap and remain in these orbitals throughout the evolution, which is a good approximation for weak interactions [23][24][25]30,31]. In that case, the occupied orbitals play the role of the sites of the spin Hamiltonian. However, because of high motional temperature in such systems, every run of the experiment typically yields a different set of populated orbitals and hence a diff...

show abstract

Beyond the Spin Model Approximation for Ramsey Spectroscopy

Cited by 6 publications

References 43 publications

Dynamics of Interacting Fermions in Spin-Dependent Potentials

Dynamics of Interacting Fermions in Spin-Dependent Potentials

Simulating fermions in spin-dependent potentials with spin models on an energy lattice

Realizing exactly solvableSU(N)magnets with thermal atoms

Contact Info

Product

Resources

About