Andrew Koller

Spin–orbit-coupled fermions in an optical lattice clock

Engineered spin–orbit coupling (SOC) in cold-atom systems can enable the study of new synthetic materials and complex condensed matter phenomena. However, spontaneous emission in alkali-atom spin–orbit-coupled systems is hindered by heating, limiting the observation of many-body effects and motivating research into potential alternatives. Here we demonstrate that spin–orbit-coupled fermions can be engineered to occur naturally in a one-dimensional optical lattice clock. In contrast to previous SOC experiments, here the SOC is both generated and probed using a direct ultra-narrow optical clock transition between two electronic orbital states in 87Sr atoms. We use clock spectroscopy to prepare lattice band populations, internal electronic states and quasi-momenta, and to produce spin–orbit-coupled dynamics. The exceptionally long lifetime of the excited clock state (160 seconds) eliminates decoherence and atom loss from spontaneous emission at all relevant experimental timescales, allowing subsequent momentum- and spin-resolved in situ probing of the SOC band structure and eigenstates. We use these capabilities to study Bloch oscillations, spin–momentum locking and Van Hove singularities in the transition density of states. Our results lay the groundwork for using fermionic optical lattice clocks to probe new phases of matter.

Quenching to unitarity: Quantum dynamics in a three-dimensional Bose gas

We study the dynamics of a dilute Bose gas at zero temperature following a sudden quench of the scattering length from a noninteracting Bose condensate to unitarity (infinite scattering length). We apply three complementary approaches to understand the momentum distribution and loss rates. First, using a time-dependent variational ansatz for the many-body state, we calculate the dynamics of the momentum distribution. Second, we demonstrate that, at short times and large momenta compared to those set by the density, the physics can be well understood within a simple, analytic two-body model. We derive a quantitative prediction for the evolution of Tans contact, which increases linearly at short times. We also study the three-body losses at finite densities. Consistent with experiments, we observe lifetimes which are long compared to the dynamics of large momentum modes.

Dynamics of Interacting Fermions in Spin-Dependent Potentials

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 Letter, 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.

Realizing exactly solvable SU(N) magnets with thermal atoms

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.

Demagnetization dynamics of noninteracting trapped fermions

Motivated by several experimental efforts to understand spin diffusion and transport in ultracold fermionic gases, we study the spin dynamics of initially spin-polarized ensembles of harmonically trapped non-interacting spin-1/2 fermionic atoms, subjected to a magnetic field gradient. We obtain simple analytic expressions for spin observables in the presence of both constant and linear magnetic field gradients, with and without a spin-echo pulse, and at zero and finite temperatures. The analysis shows the relevance of spin-motional coupling in the non-interacting regime where the demagnetization decay rate at short times can be faster than the experimentally measured rates in the strongly interacting regime under similar trapping conditions. Our calculations also show that particle motion limits the ability of a spin-echo pulse to remove the effect of magnetic field inhomogeneity, and that a spin-echo pulse can instead lead to an increased decay of magnetization at times comparable to the trapping period.

Emergence of reflectionless scattering from linearizations of integrable PDEs around solitons

We present four examples of integrable partial differential equations (PDEs) of mathematical physics that---when linearized around a stationary soliton---exhibit scattering without reflection at {\it all} energies. Starting from the most well-known and the most empirically relevant phenomenon of the transparency of one-dimensional bright bosonic solitons to Bogoliubov excitations, we proceed to the sine-Gordon, Korteweg-de Vries, and Liouvilles equation whose stationary solitons also support our assertion. The proposed connection between integrability and reflectionless scattering seems to span at least two distinct paradigms of integrability: S-integrability in the first three cases, and C-integrability in the last one. We argue that the transparency of linearized integrable PDEs is necessary to ensure that they can support the transparency of stationary solitons in the original integrable PDEs. As contrasting cases, the analysis is further extended to cover two non-integrable systems: a sawtooth-Gordon and a

Beyond the Spin Model Approximation for Ramsey Spectroscopy

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Synthetic Spin-Orbit Coupling in an Optical Lattice Clock

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Exploring collective spin dynamics in a weakly interacting gas of fermions

Ramsey spectroscopy has become a powerful technique for probing nonequilibrium dynamics of internal (pseudospin) degrees of freedom of interacting systems. In many theoretical treatments, the key to understanding the dynamics has been to assume the external (motional) degrees of freedom are decoupled from the pseudospin degrees of freedom. Determining the validity of this approximation-known as the spin model approximation-has not been addressed in detail. Here we shed light in this direction by calculating Ramsey dynamics exactly for two interacting spin-1/2 particles in a harmonic trap. We focus on s-wave-interacting fermions in quasi one- and two-dimensional geometries. We find that in one dimension the spin model assumption works well over a wide range of experimentally relevant conditions, but can fail at time scales longer than those set by the mean interaction energy. Surprisingly, in two dimensions a modified version of the spin model is exact to first order in the interaction strength. This analysis is important for a correct interpretation of Ramsey spectroscopy and has broad applications ranging from precision measurements to quantum information and to fundamental probes of many-body systems.