We investigate the spatially dependent relative phase evolution of an elongated two-component Bose-Einstein condensate. The pseudospin-$\frac{1}{2}$ system is comprised of the $|F=1,m_F=-1⟩$ and $|F=2,m_F=+1⟩$ hyperfine ground states of ${}^{87}\text{R}\text{b}$, which we magnetically trap and interrogate with radio-frequency and microwave fields. We probe the relative phase evolution with Ramsey interferometry and observe a temporal decay of the interferometric contrast well described by a mean-field formalism. Inhomogeneity of the collective relative phase dominates the loss of interferometric contrast, rather than decoherence or phase diffusion. We demonstrate a technique to simultaneously image each state, yielding subpercent variations in the measured relative number while preserving the spatial mode of each component. In addition, we propose a spatially sensitive interferometric technique to image the relative phase.

Relativistic optical rectification is analyzed by utilizing the analytical solutions of the three-dimensional collective electron motion driven by a high-intensity pulsed Gaussian beam. Under the paraxial expansion the slowly varying components in the nonlinear oscillation of electron density and electric current are extracted from the solutions first, and then they are used in the Maxwell equations as the source terms to calculate the terahertz electromagnetic fields as functions of the spatiotemporal amplitude of the pulsed Gaussian beam. The analysis compares well with available experimental data and computer simulations and demonstrates the general scheme of paraxial expansion for the analysis of relativistic nonlinear optical interactions.

We study the time dynamics of a single boson coupled to a bath of two-level systems (spins 1/2) with different excitation energies, described by an inhomogeneous Dicke model. Analyzing the time-dependent Schrödinger equation exactly, we find that at resonance the boson decays in time to an oscillatory state with a finite amplitude characterized by a single Rabi frequency if the inhomogeneity is below a certain threshold. In the limit of small inhomogeneity, the decay is suppressed and exhibits a complex (mainly Gaussian-like) behavior, whereas the decay is complete and of exponential form in the opposite limit. For intermediate inhomogeneity, the boson decay is partial and governed by a combination of exponential and power laws.

We propose a method for converting a laser into a phase-bistable system by means of the injection of an appropriately shaped monochromatic signal beam. We demonstrate, numerically and analytically, that lasing in the fundamental, ${\text{TEM}}_{00}$ mode can become phase bistable when a signal with the shape of the ${\text{TEM}}_{10}$ mode, but whose frequency is near that of the fundamental, is injected.

By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored nonstandard statistical properties. The renewal approach is defined by a set of disruptive events, consisting in the action of a completely positive superoperator over the system density matrix. The random time intervals between events are described by an arbitrary waiting-time distribution. We show that, in contrast to the Markovian case, if one performs a system preparation (measurement) at an arbitrary time, the subsequent evolution of the density-matrix evolution is modified. The nonstationary character refers to the absence of an asymptotic master equation even when the preparation is performed at arbitrary long times. In spite this property, we demonstrate that operator expectation values and operators correlations have the same dynamical structure, establishing the validity of a nonstationary quantum regression hypothesis. The nonstationary property of the dynamics is also analyzed through the response of the system to an external weak perturbation.

We derive a Bell inequality based on a generalized quasiprobability function, which is parametrized by one nonpositive real value. Two types of known Bell inequalities formulated in terms of the Wigner and the $Q$ functions are included as limiting cases. We investigate violations of our Bell inequalities for single-photon entangled states and two-mode squeezed vacuum states when varying the detector efficiency. We show that the Bell inequality for the $Q$ function allows the lowest detection efficiency for violations of local realism.

The properties of quantum mechanics with a discrete phase space are studied. The minimum uncertainty states are found and these states become the Gaussian wave packets in the continuum limit. With a suitably chosen Hamiltonian that gives free particle motion in the continuum limit, it is found that full or approximate periodic time evolution can result. This represents an example of revivals of wave packets that in the continuum limit is the familiar free particle motion on a line. Finally we examine the uncertainty principle for discrete phase space and obtain the correction terms to the continuum case.

We show that bipartite entanglement distribution (or entanglement of assistance) in multipartite quantum systems is by nature polygamous. We first provide an analytical upper bound for the concurrence of assistance in bipartite quantum systems and derive a polygamy inequality of multipartite entanglement in arbitrary-dimensional quantum systems.

We have studied numerically the evolution of an adiabatic quantum computer in the presence of a Markovian Ohmic environment by considering Ising spin-glass systems with up to 20 qubits independently coupled to this environment via two conjugate degrees of freedom. The required computation time is demonstrated to be of the same order as that for an isolated system and is not limited by the single-qubit decoherence time $T_2^{\ast }$, even when the minimum gap is much smaller than the temperature and decoherence-induced level broadening. For small minimum gap, the system can be described by an effective two-state model coupled only longitudinally to environment.

We propose a continuous-variable quantum interface that transfers an arbitrary unknown quantum state between a well-controllable source oscillator and a weakly controllable noisy target oscillator through an arbitrary Gaussian coupling. The unit fidelity of transfer is achieved by the preprocessing of the source state involving an ancillary system, collective measurement of the source after the coupling together with the ancilla, and by a subsequent feed-forward correction of the target. Particularly, these techniques allow the transfer of quantum states of light to arbitrarily noisy matter systems.

We present a method for tracking time-dependent entanglement between different modes of a quantum system as measured by observers in different states of relative (nonuniform) motion. By describing states on a given spacelike hypersurface, observers or detectors in different states of motion can detect different modes of excitation in a quantum field at any desired instant and thereby track various measures of entanglement as function of time. We illustrate our method for a scalar field, showing how entanglement degrades as a function of time if one observer begins in a state of inertial motion but ends in a state of uniform acceleration while the other remains inertial.

Relativistic and electron correlation effects are investigated for the closed-shell superheavy-element monohydrides RgH, $112{\text{H}}^{+}$, 113H, $114{\text{H}}^{+}$, 117H, $118{\text{H}}^{+}$, 119H, and $120{\text{H}}^{+}$. Periodic trends are discussed by comparing the calculated properties to the ones for the lighter elements. The size of the relativistic effects varies considerably between the different molecules with the $s$-block elements being dominated by scalar relativistic effects and the $p$-block elements dominated by spin-orbit effects. In most cases, relativistic effects are more important than electron correlation effects and both are nonadditive as one expects. $120{\text{H}}^{+}$ behaves in a counterintuitive way as it shows a relativistic bond-length expansion together with a large relativistic decrease in the dissociation energy. The reason behind this anomalous behavior is due to the relativistically diminished valence-$7d$ participation in the 120-H bond.

We analytically investigate superfluid phase in two dimension at zero temperature for asymmetric Fermi gas. Analytic expressions for both gap and chemical potentials at mean-field level are obtained as a function of binding energy and population imbalance when mass of different types of fermions is equal. We identify regions corresponding to normal, Sarma phase for different polarization, or mass ratio and discuss topological phase diagram in the BCS-BEC crossover and find that energy gap and chemical potential behave differently in these topological quantum phase. We also obtain the low-frequency and long-wavelength collective excitation spectrum and find sound velocity has a maximum when two types of mass are equal.

We study the entanglement dynamics in a two-spin system governed by a bilinear Hamiltonian and assisted by phase kicks. It is found that the application of instant kicks to both spins at some specific moments leads to enhancement of entanglement. This procedure also improves the transient character of entanglement leading, for large spins, to a formation of a plateau for the $I$ concurrence. We have numerically investigated the spin-spin dynamics for several values of spins and observed a substantial enhancement of entanglement in comparison to the evolution without kicks.

We show that some composite pulses widely employed in NMR experiments are regarded as nonadiabatic geometric quantum gates with Aharanov-Anandan phases. Thus, we reveal the presence of a fundamental issue on quantum mechanics behind a traditional technique. To examine the robustness of such composite pulses against fluctuations, we present a simple noise model in a two-level system. Then, we find that the composite pulses possesses purely geometrical nature even under a certain type of fluctuations.

We propose to use a quantized version of coherent two-color photoassociation to realize a hybrid device for quantum control of light. The dynamical features of this system are exhibited, including the slowing down or storage of light and the molecular matter-wave solitons. This may indicate a hybrid atom-molecule quantum device for storage and retrieve of optical information.

It is shown that free electrons on the helicoidal surface are affected by an effective potential, which vanishes in the $s$ channel and gives rise to both metastable as well as stable bound states. The effective potential depends linearly on the “angular momentum” quantum number and the spin state resulting in a partially nondegenerate energy spectrum. The vanishing of the potential in the $s$ channel illustrates a “miraculous” exact cancellation which is present for all quantum states. An attractive effective potential term arising from the spin connection cancels exactly a repulsive potential term, which is identical to the potential which affects relativistic bosons on the helicoidal surface.

We study the quantum kicked rotor in resonance subjected to a unitary noise defined through Kraus operators. We show that this type of decoherence does not, in general, lead to the classical diffusive behavior. We find exact analytical expressions for the density matrix and the variance in the primary resonances. The variance does not loose its ballistic behavior; however, the coherence decays as a power law. The secondary resonances are treated numerically, obtaining a power-law decay for the variance and an exponential-law decay for the coherence.

Symmetric extendibility of quantum states has recently drawn attention in the context of quantum cryptography to judge whether quantum states shared between two distant parties can be purified by means of one-way error correction protocols. In this paper we study the symmetric extendibility in a specific class of two-qudit states, i.e., states composed of two $d$-level systems, in order to find upper bounds on tolerable error rates for a wide class of qudit-based quantum cryptographic protocols using two-way error correction. In important cases these bounds coincide with previously known lower bounds, thereby proving sharpness of these bounds in arbitrary finite-dimensional systems.

A problem of three one-dimensional bosons with resonant multichannel interactions is considered. The problem is reduced to a single-channel Faddeev-Lovelace equation by elimination of the closed and output channels. The equation is regularized using algebraic properties of their singularities.