We show how the property of dualism, which can exist in the entanglement of identical particles, can be tested in the usual photonic Bell measurement apparatus with minor modifications. Two different sets of coincidence measurements on the same experimental setup consisting of a Hong-Ou-Mandel interferometer demonstrate how the same two-photon state can emerge entangled in the polarization or the momentum degree of freedom depending on the dynamical variables used for labeling the particles. Our experiment demonstrates how the same source can be used as both a polarization entangled state as well as a dichotomic momentum entangled state shared between distant users Alice and Bob in accordance with which sets of detectors they access. When the particles become distinguishable by letting the information about one of the variables be imprinted in yet another (possibly inaccessible) system or degree of freedom, the feature of dualism is expected to vanish. We verify this feature by polarization decoherence (polarization information in the environment) or arrival time difference, which both respectively destroy one of the dual forms of entanglement.

We consider a protocol to entangle an electromagnetic pulse with a mechanical oscillator at high temperature. We show this protocol to be capable of entangling currently existing experimental systems at relatively high (above the available cryostat) temperatures of the mechanical part. We also predict a possibility of conditional squeezing of the mechanical mode below the shot noise level at the cryostat temperatures.

We analyze the generation of linear-optical cluster states (LOCSs) via sequential addition of one and two qubits. Existing approaches employ the stochastic linear-optical two-qubit controlled-Z (cz) gate with success rate of $\frac{1}{9}$ per operation. The question of optimality of the cz gate with respect to LOCS generation has remained open. We report that there are alternative schemes to the cz gate that are exponentially more efficient and show that sequential LOCS growth is indeed globally optimal. We find that the optimal cluster growth operation is a state transformation on a subspace of the full Hilbert space. We show that the maximal success rate of postselected entangling $n$ photonic qubits or $m$ Bell pairs into a cluster is ${\left(\frac{1}{2}\right)}^{n-1}$ and ${\left(\frac{1}{4}\right)}^{m-1}$, respectively, with no ancilla photons, and we give an explicit optical description of the optimal mode transformations.

We present a detailed theoretical study of two-photon above-threshold excitation to the lowest dipole forbidden ${}^1{S}^e$ and ${}^1{D}^e$ autoionizing states of helium with free-electron-laser pulses. We consider the case where the formation of these transient states is detected by monitoring the yield of atoms in the metastable $1s2s$ states, which are reached in the radiative cascade decays of the autoionizing states. We describe the two-photon near-resonant driving with an effective Hamiltonian operator within the density matrix formalism, and we report the relevant parameters of the model, such as the field-induced shifts, the effective Rabi frequencies, and the cascade branching ratios of both the autoionizing states and the $1sn\ell$ states, to which the autoionizing states decay. We compare the calculated metastable atom yield to the vacuum ultraviolet florescence yield and to the electron yield. We discuss the effects of the intensity of the source, admixture of higher harmonics in the incident beam, polarization of the incident light, and the pulse chirp on the metastable atom yield.

The weak-field asymptotic theory (WFAT) of tunneling ionization including the first-order correction terms is validated for molecules by comparison with accurate calculations of molecular Siegert states in a static electric field. Both fundamental observables related to tunneling ionization, namely, the ionization rate and transverse momentum distribution of the ionized electrons, are considered. This complements our previous study of atoms [V. H. Trinh et al., Phys. Rev. A 87, 043426 (2013)]. Similarly to the atomic case, the first-order terms essentially improve the agreement between the WFAT and accurate results in a wide interval of fields up to the onset of over-the-barrier ionization. This establishes the WFAT including the first-order correction terms as an appealing alternative to accurate calculations in the tunneling regime. In addition to demonstrating the quantitative performance of the WFAT, the theory is shown to be helpful for understanding the field and orientation dependencies of the observables. In particular, we show that the first-order terms account for a deviation of the shape of the orientation dependence of the ionization rate of a molecule from that of the ionizing orbital as the field grows, which has important implications for strong-field molecular imaging techniques. This prediction of the WFAT is confirmed by comparison with time-dependent calculations.

Brownian motion is ballistic on short time scales and diffusive on long time scales. Our theoretical investigations indicate that one can observe the exact opposite—an “anomalous diffusion process” where initially diffusive motion becomes ballistic on longer time scales—in an ultracold atomic system with a size comparable to macromolecules. This system is the center-of-mass motion of a quantum matter-wave bright soliton for which the dominant source of decoherence is three-particle losses. Our simulations show that such unusual center-of-mass dynamics should be observable on experimentally accessible time scales.

Five-component minimum-energy bound states and mobile vector solitons of a spin-orbit-coupled quasi-one-dimensional hyperfine-spin-2 Bose-Einstein condensate are studied using the numerical solution and variational approximation of a mean-field model. Two distinct types of solutions with single-peak and multipeak density distribution of the components are identified in different domains of interaction parameters. From an analysis of Galilean invariance and time-reversal symmetry of the Hamiltonian, we establish that vector solitons with multipeak density distribution preserve time-reversal symmetry, but they cannot propagate while maintaining the shape of individual components. However, those with single-peak density distribution violate time-reversal symmetry of the Hamiltonian, but they can propagate with a constant velocity and maintain the shape of individual components.

We report on two types of quantum calculations pertaining to a ring of ultracold and identical bosonic ions in a static, external magnetic field. The purpose of these calculations is to give examples of what could be expected in certain types of measurements of the rotation of this ring. The first type of calculation explores how well the ring reaches the rotational ground state when it starts in the ground state of a trapping potential that is then adiabatically switched off; the trapping potential is designed to frustrate the rotation and raise the energy scale to the point where standard cooling techniques could reach the ground state. The second type of calculation shows what kind of rotation signal might be measured using two types of measuring schemes. The focus is on how the signal changes with the temperature of the ring and with how the measurement is performed.

We study the effect of thermal and quantum fluctuations on the dynamical response of a one-dimensional, strongly interacting Bose gas in a tight atomic waveguide. We combine the Luttinger liquid theory at arbitrary interactions and the exact Bose-Fermi mapping in the Tonks-Girardeau impenetrable-boson limit to obtain the dynamic structure factor of the strongly interacting fluid at finite temperature. Then we determine the drag force felt by a potential barrier moving along the fluid in the experimentally realistic situation of finite barrier width and temperature.

We investigate the connection between thermal light and coherent pulses, constructing mixtures of single pulses that yield the same first-order, equal-space-point correlation function as thermal light. We present mixtures involving (i) pulses with a Gaussian line shape and narrow bandwidths and (ii) pulses with a coherence time that matches that of thermal light. We characterize the properties of the mixtures and pulses. Our results introduce an alternative description of thermal light in terms of multifrequency coherent states, valid for the description of broadband linear light-matter interactions. We anticipate our results will be relevant to time-resolved measurements that aim to probe the dynamics of systems as if they were excited by natural thermal light.

A natural atom placed into a cavity with time-dependent parameters can be parametrically excited due to interaction with the quantized photon mode. One of the channels for this process is the dynamical Lamb effect, induced by a nonadiabatic modulation of the atomic-level Lamb shift. However, in experiments with natural atoms it is quite difficult to isolate this effect from other mechanisms of atom excitation. We point out that a transmission line cavity coupled with a superconducting qubit (an artificial macroscopic atom) provides a unique platform for observation of the dynamical Lamb effect. A key idea is to exploit a dynamically tunable qubit-resonator coupling, which was implemented quite recently. By varying the coupling nonadiabatically, it is possible to parametrically excite a qubit through a nonadiabatic modulation of the Lamb shift, even if the cavity was initially empty. The dynamics of such a coupled system is studied within the Rabi model with a time-dependent coupling constant and beyond the rotating-wave approximation. An efficient method to increase the effect through the periodic and nonadiabatic switching of the qubit-resonator coupling energy is proposed.

The recent demonstration of cooling of a macroscopic silicon nitride membrane based on dissipative coupling makes dissipatively coupled optomechanical systems promising candidates for squeezing. We theoretically show that such a system in a cavity on resonance can yield good squeezing, which is comparable to that produced by dispersive coupling. We also report the squeezing resulting from the combined effects of dispersive and dissipative couplings; thus the device can be operated in one regime or the other. We derive the maximal frequency and quadrature angles needed to observe squeezing for given optomechanical coupling strengths. We also discuss the effects of temperature on squeezing.

In the Hilbert space formulation of quantum mechanics, ideal measurements of physical variables are discussed using the spectral theory of Hermitian operators and the corresponding projector-valued measures (PVMs). However, more general types of measurements require the treatment in terms of positive-operator-valued measures (POVMs). In the Hamiltonian formulation of quantum mechanics, canonical coordinates are related to PVM. In this paper the results of an analysis of various aspects of applications of POVMs in the Hamiltonian formulation are reported. Several properties of state parameters and quantum observables given by POVMs or represented in an overcomplete basis, including the general Hamiltonian treatment of the Neumark extension, are presented. An analysis of the phase operator, given by the corresponding POVMs, in the Hilbert space and the Hamiltonian frameworks is also given.

The path-integral Monte Carlo method is employed to evaluate static (hyper)polarizabilities of small hydrogen systems at finite temperature. Exact quantum statistics are obtained for hydrogen atom and hydrogen molecule immersed in homogeneous electric field. The method proves to be reliable and yields perfect agreement with known values of static polarizabilities in both adiabatic and nonadiabatic simulations. That is, we demonstrate how electronic, rotational, and vibrational contributions can be evaluated either separately or simultaneously. Indeed, at finite temperature and nonzero-field strengths we observe considerable rovibrational effects in the polarization of the hydrogen molecule. Given sufficient computational resources, the path-integral Monte Carlo method turns out to be a straightforward tool for describing and computing static polarizabilities for traditionally challenging regimes.

We present an efficient high-order-harmonic optimal control scheme for the generation of the ultrabroad supercontinuum spectrum and an isolated ultrashort attosecond pulse in gases with a two-color mid-IR laser field. The optimal control scheme is implemented using a derivative-free unconstrained optimization algorithm called NEWUOA (NEW Unconstrained Optimization Algorithm). For illustration, the high-order-harmonic generation (HHG) of a hydrogen atom is considered for optimization. It is shown that optimally shaped laser waveforms can greatly enhance and extend the HHG plateau and efficiently generate an isolated ultrashort attosecond pulse. Moreover, by performing accurate semiclassical simulations and a detailed wavelet time-frequency analysis, we found that the optimized supercontinuum harmonics corresponding to long-trajectory electrons are responsible for an isolated ultrashort 21-as pulse.

Bose-Einstein condensates made of ultracold trapped bosonic atoms have become a central venue in which interacting many-body quantum systems are studied. The ground state of a trapped Bose-Einstein condensate has been proven to be 100% condensed in the limit of infinite particle number and constant interaction parameter [Lieb and Seiringer, Phys. Rev. Lett. 88, 170409 (2002)]. The meaning of this result is that properties of the condensate, noticeably its energy and density, converge to those obtained by minimizing the Gross-Pitaevskii energy functional. This naturally raises the question whether correlations are of any importance in this limit. Here, we demonstrate both analytically and numerically that even in the infinite particle limit many-body correlations can lead to a modification of the variance of any operator compared to that expected from the Gross-Pitaevskii result. The deviation of the variance stems from its explicit dependence on terms of the reduced two-body density matrix which otherwise do not contribute to the energy and density in this limit. This makes the variance a sensitive probe of many-body correlations even when the energy and density of the system have already converged to the Gross-Pitaevskii result. We use the many-particle position and momentum operators to exemplify this persistence of correlations. Implications of this many-body effect are discussed.

The recent Aarhus experiment [Phys. Rev. A 88, 023620 (2013)] produced wave packets by applying amplitude modulation to a trapped Bose–Einstein condensate (BEC) of ${}^{87}\mathrm{Rb}$ using an optical lattice. The present paper renders a theoretical account of this experimental production of wave packets and their subsequent time evolution, focusing on a one-dimensional noninteracting bosonic system as a fundamental starting point for accurate quantum analysis. Since experimental manipulation requires efficient wave-packet creation, we introduce the “single-$Q$ Rabi model” to give a simple and reliable description of the interband transition. As a natural extension, we demonstrate enhancement of the wave-packet production by the “two-step Rabi oscillation method” using either one or two frequencies. The subsequent time evolution is affected by the intertwining of Bragg reflection and the Landau–Zener transition at each band gap, which is analyzed with the aid of a semiclassical theory [Phys. Rev. Lett. 110, 085302 (2013)].

We present here a method for the extraction of the differential phase of an atom gradiometer that exploits the correlation of the vibration signal measured by an auxiliary classical sensor, such as a seismometer or an accelerometer. We show that sensitivities close to the quantum projection noise limit can be reached, even when the vibration noise induces phase fluctuations larger than $2\pi$. This method does not require the correlation between the atomic and classical signals to be perfect and allows for an exact determination of the differential phase, with no bias. It can also be applied to other configurations of differential interferometers, such as gyrometers, conjugate interferometers for the measurement of the fine-structure constant, or differential accelerometers for tests of the equivalence principle or detection of gravitational waves.