Motivated by a recent experiment Revelle et al., [Phys. Rev. Lett. 117, 235301 (2016)] that characterized the one- to three-dimensional crossover in a spin-imbalanced ultracold gas of ${}^6\mathrm{Li}$ atoms trapped in a two-dimensional array of tunnel-coupled tubes, we calculate the phase diagram for this system by using Hartree-Fock Bogoliubov-de Gennes mean-field theory and compare the results with experimental data. Mean-field theory predicts fully-spin-polarized normal, partially-spin-polarized normal, spin-polarized superfluid, and spin-balanced superfluid phases in a homogeneous system. We use the local density approximation to obtain density profiles of the gas in a harmonic trap. We compare these calculations with experimental measurements in Revelle et al. as well as previously unpublished data. Our calculations qualitatively agree with experimentally measured densities and coordinates of the phase boundaries in the trap and quantitatively agree with experimental measurements at moderate-to-large polarizations. Our calculations also reproduce the experimentally observed universal scaling of the phase boundaries for different scattering lengths at a fixed value of scaled intertube tunneling. However, our calculations have quantitative differences with experimental measurements at low polarization and fail to capture important features of the one- to three-dimensional crossover observed in experiments. These suggest the important role of physics beyond mean-field theory in the experiments. We expect that our numerical results will aid future experiments in narrowing the search for the Fulde-Ferrell-Larkin-Ovchinnikov phase.

Motivated by recent progress on ultracold alkaline-earth atoms towards the goal of simulating Kondo physics, in this work we exactly solve the few-body problem of one and two trapped fermions in one dimension interacting with a localized impurity under tunable spin-exchange interaction. It is found that depending on the sign of the spin-exchange coupling, i.e., ferromagnetic (FM) or antiferromagnetic (AFM), the attractive and repulsive branches can hold different magnetic structures. For the two-fermion case, we demonstrate the Kondo screening effect for the attractive branch with AFM coupling, and show that such screening is absent for the ground state with FM coupling. Moreover, we find a sequence of FM upper branches in the AFM coupling side. These FM states are orthogonal to all other attractive branches and their wave functions feature a full spin-charge separation. The effect of an additional contact interaction and the extension of our results to many particles are also discussed. This work reveals the intriguing physics uniquely associated with the spin-exchange interaction in the few-body point of view, which can be readily explored in the experiment of ultracold alkaline-earth atoms.

We adopt a nonlinear two-mode model to investigate the Rosen-Zener-Stückelberg (RZS) interferometry of an interacting Bose-Einstein condensate trapped in double-well potential with a periodically modulating barrier. For symmetric potential, we analyze the properties of interference patterns and derive the interference conditions. For asymmetric potential, we explore the resonance structures caused by destructive interference at the weakly coupling limit and obtain the resonance conditions. In particular, we find that the chaotic motions in the asymmetric case with low-frequency modulation, can destroy the formation of interference fringes. In the symmetric case with high-frequency modulation, we see Fano-line-like resonance structures and find that the reso- nance positions exactly correspond to the boundary of macroscopic quantum self-trapping. We show that the nonlinearity can significantly alter both the shape and position of interference fringes and resonance structures. We discuss the experimental feasibility by comparing the solution of the Gross-Pitaevskii equation with both the solution of the two-mode model and the truncated Wigner simulation as well. The results suggest important applications of nonlinear RZS interferometry both in precisely controlling the dynamics and in accurately measuring the parameters of interacting many-body systems.

This paper quantifies the rate at which laser shot-noise energy is delivered to a nanoparticle for the various scenarios commonly encountered in levitated optomechanics. Although previous articles have the same form and dependencies, the proportionality constants often differ in the literature. This paper resolves these discrepancies. The rate at which energy is delivered to an optically trapped particle's respective degrees of freedom depends on the radiation pattern of scattered light as well as the direction of laser propagation. For a traveling plane wave with linearly polarized light in the Rayleigh regime, this leads the translational shot-noise heating rate to be proportional to 1/10 of the total rate in the laser polarization direction, 7/10 in the laser propagation direction, and 2/10 in the direction perpendicular to both. Analytical expressions for the shot-noise heating rate are provided in the Rayleigh limit as well as numerical calculations for particles in the Mie regime for silica and diamond. For completeness, numerical calculations of the shot-noise heating for silica Mie particles at the focus of a strongly focused laser beam are calculated for varying numerical aperture and common laser wavelengths. Both numerical calculations show that the Rayleigh expression generally gives an overestimate of the shot-noise heating especially for larger radii but is still a good approximation even for incident focal fields. The exception to the relative decrease is when a Mie resonance is reached which was found for diamond. Lastly, Rayleigh expressions for the rotational shot-noise heating for a symmetric toplike particle for linear, elliptically, and unpolarized light are also provided.

We show that, in an isolated two-level quantum system described by a time-dependent Hamiltonian, correlated noise in the Hamiltonian's parameters can lead to an arbitrarily long plateau in the state-preparation fidelity as a function of elapsed time. We explain the formation of this plateau by using the Bloch-sphere representation, deriving analytical expressions for its start and end times and its height. We also briefly discuss the extent to which this phenomenon is expected to be visible in more general quantum systems with $N>2$ levels.

The quantum coupling of individual superconducting qubits to microwave photons leads to remarkable experimental opportunities. Here we consider the phononic case where the qubit is coupled to an electromagnetic surface acoustic wave antenna that enables supersonic (electromagnetic) propagation of the qubit oscillations. This can be considered as a giant atom that is many phonon wavelengths long. We study an exactly solvable toy model that captures these effects, and find that this non-Markovian giant atom has a suppressed relaxation, so long as an effective vacuum coupling exists between a qubit excitation and a localized wave packet of sound, even in the absence of a cavity for the sound waves. Finally, we consider practical implementations of these ideas in current surface acoustic wave devices.

We study the scattering of photons from periodically modulated quantum-optical systems. For excitation-number-conserving quantum-optical systems, we connect the analytic structure of the frequency-domain $N$-photon scattering matrix of the system to the Floquet decomposition of its effective Hamiltonian. Furthermore, it is shown that the first-order contribution to the transmission or equal-time $N$-photon correlation spectrum with respect to the modulation frequency is completely geometric in nature, i.e., it depends only on the Hamiltonian trajectory and not on the precise nature of the modulation being applied.

We develop the formal approach to the angular spectrum transfer in parametric down-conversion that allows pumping with a structured beam. The scheme is based on an entangled photon source pumped by a laser beam structured with a vector-vortex polarization profile. This creates a two-photon quantum state exhibiting polarization-dependent transverse correlations that can be accessed through coincidence measurements on the spatially separated photons. The calculated correlations are shown to present a spin-orbit profile typical of vector beams, however, distributed on separate measurement regions. Our approach allows the design of the pump beam vector spatial structure and measurement strategies for potential applications of these entangled states, such as in quantum communication.

We present a discrete-variable quantum teleportation scheme using pulsed optomechanics. In our proposal, we demonstrate how an unknown optical input state can be transferred onto the joint state of a pair of mechanical oscillators, without physically interacting with one another. We further analyze how experimental imperfections will affect the fidelity of the teleportation and highlight how our scheme can be realized in current state-of-the-art optomechanical systems.

Controlling the dynamics of quantum systems has been a long-standing goal of quantum physics. To understand the controllability of a finite-dimensional quantum system is a fundamental problem in quantum control theory, but can be very challenging in many cases. In particular, results on controllability of open-loop coherently controlled closed quantum systems under symmetry constraints have been elusive. In this paper, we study the controllability of spin systems with some specific symmetry where spins are coupled via Ising interaction and manipulated collectively by a global control field. Based on Lie group and Lie algebra techniques, we find the conditions under which the system is universally controllable in its irreducible subspaces. We believe that the results obtained here will contribute to quantum controlling on symmetric quantum systems.

We introduce a generalization of the Pauli channels using the mutually unbiased measurement operators. The resulting channels are bistochastic, but their eigenvectors are not unitary. We analyze the channel properties, such as complete positivity, entanglement breaking, and the multiplicativity of maximal output purity. We illustrate our results with the maps constructed from the Gell-Mann matrices and the Heisenberg-Weyl observables.

The energy shifts due to interactions violating time-reversal invariance and parity symmetry, $g$ factors, and energies for the hyperfine levels of the ground rotational level of the ${}^3\mathrm{\Delta }_1$ electronic state of the ${}^{177}\mathrm{Hf}{}^{19}\mathrm{F}^{+}$ ion are calculated as functions of the external electric and magnetic fields. The calculations can be used to plan an experiment to measure the magnetic quadrupole moment of the ${}^{177}\mathrm{Hf}$ nucleus and to interpret the obtained data.

When a two-level atom interacts resonantly with a coherent electromagnetic field, the polarizability of the atom can be modulated due to the Rabi oscillations between atomic levels. We show that in the quantum vacuum, such a time-dependent atomic polarizability can lead to a resonant generation of photon pairs, a phenomenon reminiscent of photon emission in the dynamical Casimir effect (DCE). Specifically, we employ a dressing transformation to obtain an effective Hamiltonian which uncovers a polarizability-dependent parametric interaction corresponding to DCE. We determine the photon emission rate and indicate features of DCE photon pairs distinguishable from regular fluorescence photons.

We study the quantum phase transition (QPT) in a non-Hermitian Tavis-Cummings (TC) model of experimentally accessible parameters, which is engineered with two drive fields applied to an ensemble of two-level systems (TLSs) and a cavity, respectively. When the two drive fields satisfy a given parameter-matching condition, the coupled cavity-TLS ensemble system can be described by an effective standard TC Hamiltonian in the rotating frame. In this ideal Hermitian case, the engineered TC model can exhibit the super-radiant QPT with spin conservation at an experimentally accessible critical coupling strength, but the QPT is, however, spoiled by the decoherence. We find that in this non-Hermitian case, the QPT can be recovered by introducing a gain in the cavity to balance the loss of the TLS ensemble. Also, the spin-conservation law is found to be violated due to the decoherence of the system. Our study offers an experimentally realizable approach to implementing QPT in the non-Hermitian TC model.

We propose an idea of eigenstate clustering in non-Hermitian systems. We show that nonorthogonal eigenstates can be clustered around exceptional points and illustrate our idea on some models. We discuss that exponential localization of eigenstates at edges due to the non-Hermitian skin effect is a typical example of eigenstate clustering. We numerically see that clustering of localized or extended eigenstates is possible in systems with both open and closed boundaries. We show that gain and loss can enhance eigenstate clustering. We use fidelities and the standard $k$-means clustering algorithm for a systematic study of clustered eigenstates.

The thermal two-photon level broadening of the excited energy levels in the hydrogen and H-like helium is evaluated via the imaginary part of thermal two-loop self-energy correction for bound electrons. All the derivations are presented in the framework of rigorous quantum electrodynamic theory at finite temperatures and are applicable for the H-like ions. On this basis, we found a contribution to the level broadening induced by the blackbody radiation which is fundamentally different from the usual line broadening caused by the stimulated two-photon decay and the Raman scattering of thermal photons. Numerical calculations of the two-loop thermal correction to the two-photon width for the $2s$ state in hydrogen and singly ionized helium atoms show that the effect could significantly exceed the higher-order relativistic and radiative QED corrections commonly included in the calculations. In addition, the thermal two-loop self-energy correction significantly exceeds the “ordinary” stimulated one-photon depopulation rate at the relevant laboratory temperatures. In this work, detailed analysis and the corresponding comparison of the effect with the existing laboratory measurements in H-like ions are carried out.

We propose a simple scheme for implementing fast arbitrary phase gates and employ pulse modulation to improve the gate robustness against different sources of noise. Parametric driving of a cavity is introduced to induce Rabi interactions between the cavity and qutrits, and then a two-qubit arbitrary phase gate is constructed by designing proper logical states. On this basis, we implement amplitude-shaped gates to obtain enhanced resilience to control errors in gate time and frequency detuning. By virtue of specifically designed logical states, the scheme displays intrinsic resistance to the energy relaxations of qutrits. Furthermore, we show that the gate robustness against cavity decay can be enhanced significantly with amplitude modulation.

Quantum electrodynamics (QED) is currently considered to be one of the most accurate theories of fundamental interactions. As its extraordinary precision offers unique scientific opportunities, e.g., search for new physics, stringent experimental tests of QED continue to be of high importance. To this end, highly charged ions represent an exceptional test-bed due to enhanced QED effects. Recently, forbidden transitions in F-like ions have been analyzed to few ppm precision, resolving previous discrepancies between theory and experiment. Here we further test the accuracy of QED calculations with three new (Re, Os, Ir), and two improved (Kr, W) measurements of the ${}^{2}P_{1/2}\text{−}{}^{2}P_{3/2}$ transition energy in F-like ions using the NIST electron-beam ion trap and extreme-ultraviolet and x-ray spectrometers. Good agreement between theoretical and experimental energies is found for all considered elements.

Comagnetometers have been validated as valuable components of the atomic physics toolbox in fundamental and applied physics. So far, the explorations have been focused on systems involving nuclear spins. Presented here is a demonstration of an active alkali-metal (electronic) system, i.e., a dual-frequency spin maser operating with the collective cesium $F=3$ and $F=4$ spins. The experiments have been conducted in both magnetically shielded and unshielded environments. In addition to the discussion of the system's positive-feedback mechanism, the implementation of the dual-frequency spin maser for industrial nondestructive testing is shown. The stability of the $F=3$ and $F=4$ spin precession frequency ratio measurement is limited at the $3\times {10}^{-8}$ level by the laser frequency drift, corresponding to a frequency stability of $1.2\mathrm{mHz}$ for ${10}^4$ s integration time. We discuss measurement strategies that could improve this stability to nHz, enabling measurements with sensitivities to the axion-nucleon and axion-electron interactions at the levels of $f_a/C_N\sim {10}^9$ and $f_a/C_e\sim {10}^8$ GeV, respectively.

We report on experimental and theoretical investigations of the polarization dependence of magnetic resonance generated by synchronous optical pumping. Magnetic resonances with narrow linewidth are generated experimentally using a rubidium vapor cell with octadecyltrichlorosilane antirelaxation coating on inner walls. We studied the effect of light ellipticity on the amplitudes and widths of magnetic resonances by matching the light modulation frequency with $2{\mathrm{\Omega }}_L$ (alignment) and ${\mathrm{\Omega }}_L$ (orientation) in a Bell-Bloom interaction geometry, where ${\mathrm{\Omega }}_L$ corresponds to the Larmor frequency. Both $2{\mathrm{\Omega }}_L$ and ${\mathrm{\Omega }}_L$ resonance amplitudes showed a strong dependence on the light ellipticity. In addition, we showed that the duty cycle of light modulation changes the slope of amplitude variations in $2{\mathrm{\Omega }}_L$ and ${\mathrm{\Omega }}_L$ resonances with light ellipticity. As a potential application, we showed that the difference between $2{\mathrm{\Omega }}_L$ and ${\mathrm{\Omega }}_L$ resonance amplitudes can be used for in situ measurement of light ellipticity. We also studied the dependence of $2{\mathrm{\Omega }}_L$ and ${\mathrm{\Omega }}_L$ resonance amplitudes on the polarization angle of linearly polarized light. These amplitudes oscillate periodically with the polarization angle. We found this oscillatory behavior to be sensitive to the tilt in magnetic field direction from the polarization plane. Such a property could be used to realize a vector magnetometer. A density matrix based theoretical model is developed to simulate the magnetic resonance spectrum for different light polarizations. Our theoretical model accurately reproduces the above-mentioned experimental observations.