By investigating the compressibility of one-dimensional lattice fermions at various filling factors, we study the phase separation and re-entrant transition within the framework of the Bethe ansatz method. We model the system using the repulsive Hubbard model and calculate compressibility as a function of polarization for arbitrary values of chemical potential, temperature, and interaction strength. For filling factors $0<n<1$, compressibility is a nonmonotonic function of polarization at all thermodynamic parameters. The compressibility reveals a phase transition into a phase-separated state for both low and intermediate temperatures at intermediate interactions as one increases the polarization. For certain filling factors, we find the re-entrant transition into the mixed phase at a higher polarization.

Motivated by recent experiments with ultracold quantum gases in optical lattices we study the decay of the staggered moment in the one-dimensional Fermi-Hubbard model starting from a perfect Néel state using exact diagonalization and the infinite-system-size time-evolving-block-decimation method. This extends previous work in which the same problem has been addressed for pure spin Hamiltonians. As a main result, we show that the relaxation dynamics of the double occupancy and of the staggered moment are different. The former is controlled by the nearest-neighbor tunneling rate while the latter is much slower and strongly dependent on the interaction strength, indicating that spin excitations are important. This difference in characteristic energy scales for the fast charge dynamics and the much slower spin dynamics is also reflected in the real-time evolution of nearest-neighbor density and spin correlations. A very interesting time dependence emerges in the von Neumann entropy, which at short times increases linearly with a slope proportional to the tunneling matrix element while the long-time growth of entanglement is controlled by spin excitations. Our predictions for the different relaxation dynamics of the staggered moment and the double occupancy should be observable in state-of-the-art optical lattice experiments. We further compare time averages of the double occupancy to the expectation values in both the canonical and diagonal ensembles, which quantitatively disagree with each other on finite systems. We relate the question of thermalization to the eigenstate thermalization hypothesis.

We propose using an array of potential wells as an interferometer in which the beam splitters are provided by tunneling during an appropriate time through the barrier between wells. This arrangement allows demonstration of generalized Hong-Ou-Mandel effects with multiple particles traversing one or several beam splitters. Other interferometer effects can occur, including a violation of the Bell-Clauser-Horne-Shimony-Holt form of the Bell inequality. With interactions, one sees various effects, including so-called fermionization, collective tunneling, and self-trapping.

Narrow linewidth signals of electromagnetically induced transparency (EIT) in the metastable ${}^{83}\mathrm{Kr}$ have been observed. Various hyperfine transitions in the $4p^{5}5s{[3/2]}_2$ to $4p^{5}5p{[5/2]}_3$ manifolds of ${}^{83}\mathrm{Kr}$ have been identified through the experimentally observed EIT signals. Some unresolved or poorly resolved hyperfine transitions in saturated absorption spectroscopy (SAS) are clearly resolved in the present work. Using the spectral separation of these EIT identified hyperfine transitions, the magnetic hyperfine constant $\left(A\right)$ and the electric quadrupole hyperfine constant $\left(B\right)$ are determined with improved accuracy for $4p^{5}5s{[3/2]}_2$ and $4p^{5}5p{[5/2]}_3$ manifolds.

We describe the implementation of laser-cooled silica microspheres as force sensors in a dual-beam optical dipole trap in high vacuum. Using this system we have demonstrated trap lifetimes exceeding several days, attonewton force detection capability, and wide tunability in trapping and cooling parameters. Measurements have been performed with charged and neutral beads to calibrate the sensitivity of the detector. This work establishes the suitability of dual-beam optical dipole traps for precision force measurement in high vacuum with long averaging times, and enables future applications including the study of gravitational inverse square law violations at short range, Casimir forces, acceleration sensing, and quantum optomechanics.

Multipartite nonlocality is of great fundamental interest and constitutes a useful resource for many quantum information protocols. However, demonstrating it in practice, by violating a Bell inequality, can be difficult. In particular, standard experimental setups require the alignment of distant parties' reference frames, which can be challenging or impossible in practice. In this work we study the violation of certain Bell inequalities, namely the Mermin, Mermin-Klyshko, and Svetlichny inequalities, without shared reference frames, when parties share a Greenberger-Horne-Zeilinger state. Furthermore, we analyze how these violations demonstrate genuine multipartite features of entanglement and nonlocality. For three, four, and five parties, we show that it is possible to violate these inequalities with high probability, when the parties choose their measurements from the three Pauli operators, defined only with respect to their local frames. Moreover, the probability of violation, and the amount of violation, are increased when each party chooses their measurements from the four operators describing the vertices of a tetrahedron. We also consider how many randomly chosen measurement directions are needed to violate the Bell inequalities with high probability. We see that the obtained levels of violation are sufficient to also demonstrate genuine multipartite entanglement and nonseparability. Finally, we show analytically that choosing from two measurement settings per party is sufficient to demonstrate the maximum degree of genuine multipartite entanglement and nonseparability with certainty when the parties' reference frames are aligned in one direction so that they differ only in rotations around one axis.

Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes another part. Translating this scenario into both classical and quantum mechanics allows a transition to be made from a time-independent mechanics for the closed composite to a time-dependent description of the observed part alone. The use of Hamilton-Jacobi theory yields a very close parallel between the derivations in classical and quantum mechanics. The time-dependent equations, Hamilton-Jacobi or Schrödinger, appear as approximations since no observed system is truly closed. The quantum case has an additional feature in the condition that the observing environment must become classical in order to define a real classical time variable. This condition leads to a removal of entanglement engendered by the interaction between the observed system and the observing environment. Comparison is made to the similar emergence of time in quantum gravity theory.

Quantum information can be encoded in the set of steady states (SSS) of a driven-dissipative system. Nonsteady states are separated by a large dissipative gap that adiabatically decouples them while the dynamics inside the SSS is governed by an effective, dissipation-projected, Hamiltonian. The latter results from the interplay between a weak driving and the fast relaxation process that continuously projects the system back to the SSS. This amounts to a different type of environment-induced quantum Zeno effect. We prove that the dissipation-projected dynamics is of geometric nature and that it is robust against different types of Hamiltonian and dissipative perturbations. Remarkably, in some cases an effective unitary dynamics can emerge out of purely dissipative interactions.

We discuss the so-called mean king's problem, a retrodiction problem among noncommutative observables, in the context of error detection. Describing the king's measurement effectively by a single error operation, we give a solution of the mean king's problem using quantum error-correcting codes. The existence of a quantum error-correcting code from a solution is also presented.

Universal quantum simulation may provide insights into those many-body systems that cannot be described classically and that cannot be efficiently simulated with current technology. The Trotter formula, which decomposes a desired unitary time evolution of the simulator into a stroboscopic sequence of repeated elementary evolutions, is a key algorithmic component which makes quantum simulation of dynamics tractable. The Trotter number $n$ sets the time scale on which a computer running this algorithm is switched from one elementary evolution to another. In the ideal case, the precision of the simulation can be arbitrarily controlled by increasing $n$. We study a more realistic scenario where each gate is applied imperfectly. The resultant trade-off in errors leads to an ultimate limit on the precision of the simulation. We calculate the optimum Trotter number $n^{*}$ that achieves this limit, which is the minimum statistical distance from the actual simulation to the ideal one.

A recently demonstrated technique of continuous indirect pumping enables a high level of atomic spin polarization to be generated in thermal alkali-metal vapors, without compromising the coherence lifetime through power broadening from the pump laser. The indirect pumping process combines optical excitation and spin-exchange collisions. Here we describe the pumping process and the role of spin-exchange collisions for the case of amplitude-modulated optical excitation. We demonstrate that effective spin-exchange decoherence is modified by the measurement geometry and dynamics. Decoherence changes are studied through magneto-optical-rotation signals. The studies presented here are particularly important for optimizing the performance of an atomic magnetometer operating in the quantum nondemolition configuration in a nonzero-magnetic-field environment.

We report the achievement of stimulated Raman adiabatic passage (STIRAP) in the microwave frequency range between internal states of a Bose-Einstein condensate magnetically trapped in the vicinity of an atom chip. The STIRAP protocol used in this experiment is robust to external perturbations as it is an adiabatic transfer and power efficient as it involves only resonant (or quasiresonant) processes. Taking into account the effect of losses and collisions in a nonlinear Bloch equations model, we show that the maximum transfer efficiency is obtained for nonzero values of the one- and two-photon detunings, which is confirmed quantitatively by our experimental measurements.

We present an experimental investigation of ultrafast laser-driven Rabi oscillations of atomic rubidium. Because the broadband spectrum of an ultrafast laser pulse simultaneously couples all of the electronic hyperfine transitions between the excited and ground states, the complex excitation linkages involved with the $D_1$ or $D_2$ transition are energy degenerate. By application of the Morris-Shore transformation, this study shows that the considered multistate system is reduced to a set of independent two-state systems and dark states. In experiments performed by ultrafast laser interactions of atomic rubidium in the strong interaction regime, we demonstrate that the ultrafast dynamics of the considered system are governed by no more than two decoupled Rabi oscillations when it interacts with ultrafast laser pulses of any polarization state. We further show the implications of this result with regard to possible control of photoelectron polarizations.

Photoionization cross sections and dipole angular distribution asymmetry parameters, β, of $5s$ and $4d$ shells of the closed-shell ions $({\mathrm{La}}^{3+},{\mathrm{La}}^{9+}$, and ${\mathrm{La}}^{11+})$ in the La isonuclear sequence have been studied using the relativistic random phase approximation. The positions of the $5s$ Cooper minima in ${\mathrm{La}}^{3+}$ and ${\mathrm{La}}^{9+}$ ions are found to be extremely sensitive to the details of electron correlation. The results show that the $5s$ cross sections of ${\mathrm{La}}^{3+}$ and ${\mathrm{La}}^{9+}$ do not lie along the same curve near the thresholds; the $4d$ cross sections, however, do match well in overlap regions so they lie along the same curve, over the isonuclear sequence, except for a shift in threshold towards higher energies with increasing degree of ionization.

Thanks to the recent experimental realization and control of artificial gauge fields, spin-orbit (SO) couplings are witnessing an ever increasing interest in the field of cold atoms. However, predicting their effect on spin polarization and energetic properties of interacting systems is a major challenge, due to the complex interplay between spin and position dynamics. In this work we exploit the diffusion Monte Carlo algorithm to compute energetic and polarization properties of a three-dimensional repulsive Fermi gas in the presence of Rashba spin-orbit coupling. We find that SO effects tend to contrast the spin alignment induced by the exchange interaction, slightly shifting the onset of the Stoner instability towards larger values of the scattering length. In addition, polarization and energy properties of the system can be tuned trough a combined control of the repulsive interaction and Rashba coupling.

A trapped atom interferometer involving state-selective adiabatic potentials with two microwave frequencies on a chip is proposed. We show that this configuration provides a way to achieve a high degree of symmetry between the two arms of the interferometer, which is necessary for coherent splitting and recombination of thermal (i.e., noncondensed) atoms. The resulting interferometer holds promise to achieve high contrast and long coherence time, while avoiding the mean-field interaction issues of interferometers based on trapped Bose-Einstein condensates.

We present a variational study of pseudo-spin-$1/2$ Bose gases in a harmonic trap with weak three-dimensional (3D) spin-orbit coupling of $\mathbf{\sigma }·\mathbf{p}$ type. This spin-orbit coupling mixes states with different parities, which inspires us to approximate the single-particle state with the eigenstates of the total angular momentum, i.e., superposition of harmonic $s$-wave and $p$-wave states. As the time-reversal symmetry is protected by two-body interaction, we set the variational order parameter as the combination of two mutually time-reversal symmetric eigenstates of the total angular momentum. The variational results essentially reproduce the 3D skyrmionlike ground state recently identified by Kawakami et al. [T. Kawakami, T. Mizushima, M. Nitta, and K. Machida, Phys. Rev. Lett. 109, 015301 (2012)]. We show that these skyrmionlike ground states emerging in this model are primarily caused by the $p$-wave spatial mode involved in the variational order parameter that drives two spin components spatially separated. We find the ground state of this system falls into two phases with different density distribution symmetries depending on the relative magnitude of intraspecies and interspecies interaction: phase I has parity symmetric and axisymmetric density distributions, while phase II is featured with special joint symmetries of discrete rotational and time-reversal symmetry. With the increasing interaction strength the transition occurs between two phases with distinct density distributions, while the topological 3D skyrmionlike spin texture is symmetry protected.

The dynamics of a single impurity interacting with a many-particle background is one of the central problems of condensed-matter physics. Recent progress in ultracold-atom experiments makes it possible to control this dynamics by coupling an artificial gauge field specifically to the impurity. In this paper, we consider a narrow toroidal trap in which a Fermi gas is interacting with a single atom. We show that an external magnetic field coupled to the impurity is a versatile tool to probe the impurity dynamics. Using a Bethe ansatz, we calculate the eigenstates and corresponding energies exactly as a function of the flux through the trap. Adiabatic change of flux connects the ground state to excited states due to flux quantization. For repulsive interactions, the impurity disturbs the Fermi sea by dragging the fermions whose momentum matches the flux. This drag transfers momentum from the impurity to the background and increases the effective mass. The effective mass saturates to the total mass of the system for infinitely repulsive interactions. For attractive interactions, the drag again increases the effective mass which quickly saturates to twice the mass of a single particle as a dimer of the impurity and one fermion is formed. For excited states with momentum comparable to number of particles, effective mass shows a resonant behavior. We argue that standard tools in cold-atom experiments can be used to test these predictions.

We show that the description of light in terms of Stokes operators in combination with the assumption of Gaussian statistics results in a dramatic simplification of the experimental study of fluctuations in the light transmitted through an atomic vapor: no local oscillator is required, the detected quadrature is easily selected by a wave-plate angle, and the complete noise ellipsis reconstruction is obtained via matrix diagonalization. We provide empirical support for the assumption of Gaussian statistics in quasiresonant light transmitted through an ${}^{87}\mathrm{Rb}$ vapor cell and we illustrate the suggested approach by studying the evolution of the fluctuation ellipsis as a function of laser detuning. Applying the method to two light beams obtained by parting squeezed light in a beam splitter, we have measured the entanglement and quantum Gaussian discord.