Plane waves and cylindrical or spherical vortex modes are important sets of solutions of quantum and classical wave equations. These are eigenmodes of the energy-momentum and angular-momentum operators, i.e., generators of spacetime translations and spatial rotations, respectively. Here we describe another set of wave modes: eigenmodes of the “boost momentum” operator, i.e., a generator of Lorentz boosts (spatiotemporal rotations). Akin to the angular momentum, only one (say, $z)$ component of the boost momentum can have a well-defined quantum number. The boost eigenmodes exhibit invariance with respect to the Lorentz transformations along the $z$ axis, leading to scale-invariant wave forms and steplike singularities moving with the speed of light. We describe basic properties of the Lorentz-boost eigenmodes and argue that these can serve as a convenient basis for problems involving causal propagation of signals.

In quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present an algorithm for preparing particle states to use in simulation of fermionic quantum field theory (QFT) on a quantum computer, which is based on the matrix product state ansatz. We apply this to the massive Gross-Neveu model in one spatial dimension to illustrate the algorithm, but we believe the same algorithm with slight modifications can be used to simulate any one-dimensional massive fermionic QFT. In the case where the number of particle species is 1, our algorithm can prepare particle states using $O\left({\epsilon }^{-3.23...}\right)$ gates, which is much faster than previous known results, namely, $O\left({\epsilon }^{-8-o\left(1\right)}\right)$. Furthermore, unlike previous methods which were based on adiabatic state preparation, the method given here should be able to simulate quantum phases unconnected to the free theory.

We put forward a hybrid quantum key distribution protocol based on coherent states, Gaussian modulation, and photon-number-resolving (PNR) detectors, and show that it may enhance the secret key generation rate (KGR) compared to homodyne-based schemes. Improvement in the KGR may be traced back to the dependence of the two-dimensional discrete output variable on both the input quadratures, thus overcoming the limitations of the original protocol. When reverse reconciliation is considered, the scheme based on PNR detectors outperforms the homodyne one both for individual and collective attacks. In the presence of direct reconciliation, the PNR strategy is still the best one against individual attacks, but for the collective ones the homodyne-based scheme is still to be preferred as the channel transmissivity decreases.

An arbitrary qubit can be transmitted through a spin chain by perturbatively coupling both communicating parties to it. These so-called weak-coupling models rely on effective Rabi oscillations between the outer spins, yielding nearly maximum fidelity while offering great resilience against disorder with the cost of having long transfer times. Considering that framework, here we address a one-dimensional nonsymmetric channel connecting two spins, one placed at each end of it. Given any pattern of nearest-neighbor coupling strengths, we obtain an analytical expression that accounts for the effective long-range interaction between them and study the interplay between transfer time and fidelity. Furthermore, we show that homogeneous channels provide the best speed-fidelity tradeoff.

Long-time behavior of a unitary quantum gate $U$, acting sequentially on two subsystems of dimension $N$ each, is investigated. We derive an expression describing an arbitrary iteration of a two-qubit gate making use of a link to the dynamics of a free particle in a three-dimensional (3D) billiard. Due to ergodicity of such a dynamics an average along a trajectory $V^t$ stemming from a generic two-qubit gate $V$ in the canonical form tends for a large $t$ to the average over an ensemble of random unitary gates distributed according to the flat measure in the Weyl chamber—the minimal 3D set containing points from all orbits of locally equivalent gates. Furthermore, we show that for a large dimension $N$ the mean entanglement entropy averaged along a generic trajectory coincides with the average over the ensemble of random unitary matrices distributed according to the Haar measure on $\text{U}\left(N^2\right)$.

We investigate molecular photoelectron-momentum distribution (MPMD) and molecular photoelectron angular distribution (MPAD) of oriented ${\mathrm{H}}_2{}^{+}$ under frozen-nuclei approximation driven by elliptically polarized laser pulse by numerically solving a two-dimensional time-dependent $\mathrm{Schr}\ddot{\mathrm{o}}\mathrm{dinger}$ equation. The results show that the MPMDs and MPADs are sensitive to the internuclear distance, which is illustrated by the initial MPMDs and the evolution of MPMDs. In addition, they are also dependent on laser ellipticity and wavelength. When the laser wavelength is $5\mathrm{nm}$, the phenomenon of laser-induced electron diffraction can be observed in both MPMD and MPAD.

We present a detailed analysis of a robust and fast laser cooling scheme [J. Cerrillo et al., Phys. Rev. Lett. 104, 043003 (2010)] on a three-level system. A special laser configuration, applicable to trapped ions, atoms, or cantilevers, designs a double-path quantum interference that eliminates the blue sideband in addition to the carrier transition, thus excluding any heating process involving up to one-phonon interactions. As a consequence, cooling achieves vanishing phonon occupation up to first order in the Lamb-Dicke parameter expansion. Underlying this scheme is a combined action of two cooling schemes which makes the proposal very flexible under constraints of the physical parameters such as laser intensity, detuning, or optical access, making it a viable candidate for experimental implementation. Furthermore, it is considerably faster than existing ground state cooling schemes. Its suitability as a cooling scheme for several ions in a trap and three-dimensional cooling is shown.

The quantum-mechanical states of neutral particles endowed with the magnetic moment (such as neutrons, light atoms, or even neutrinos, although the effect will be extremely tiny) in the combination of electromagnetic vortex field together with the constant magnetic field are investigated. It is shown that this system of fields is in principle capable of capturing the particle in the perpendicular direction and guiding it along the propagating wave. The quantum evolution is subject to tunneling processes, which can destroy the delicate trapping mechanism. The calculated probability of such processes shows that basically it should be possible to catch and guide the particle for the time corresponding to about ${10}^5{\omega }^{-1}$, where $\omega$ is the frequency of the guiding wave. This time can be lengthened by the appropriate adjustments of the external magnetic field. Due to the very small values of magnetic moments of available neutral particles and their relatively large masses, this binding mechanism constitutes presently only a theoretical possibility since it would require extremely strong magnetic fields.

We establish a theoretical framework for exploring the quantum dynamics of finite ultracold bosonic ensembles based on the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy for equations of motion for few-particle reduced density matrices (RDMs). The theory applies to zero as well as low temperatures and is formulated in a highly efficient way by utilizing dynamically optimized single-particle basis states and representing the RDMs in terms of permanents with respect to those. An energy, RDM compatibility, and symmetry conserving closure approximation is developed on the basis of a recursively formulated cluster expansion for these finite systems. In order to enforce necessary representability conditions, two minimally invasive and energy-conserving correction algorithms are proposed, involving the dynamical purification of the solution of the truncated BBGKY hierarchy and the correction of the equations of motion themselves, respectively. For gaining conceptual insights, the impact of two-particle correlations on the dynamical quantum depletion is studied analytically. We apply this theoretical framework to both a tunneling and an interaction-quench scenario. Due to our efficient formulation of the theory, we can reach truncation orders as large as twelve and thereby systematically study the impact of the truncation order on the results. While the short-time dynamics is found to be excellently described with controllable accuracy, significant deviations occur on a longer timescale in sufficiently far off-equilibrium situations. Theses deviations are accompanied by exponential-like instabilities leading to unphysical results. The phenomenology of these instabilities is investigated in detail and we show that the minimally invasive correction algorithm of the equation of motion can indeed stabilize the BBGKY hierarchy truncated at the second order.

We show that quantum coherence produces an observable many-body signature in the dynamics of few-fermion Hubbard systems (describing cold atoms in optical lattices, coupled quantum dots, or small molecules) in the form of a revival in the transition probabilities echoing a flip of the system's itinerant spins. Contrary to its single-particle (Hahn) version, this many-body spin echo is not dephased by strong interactions or spin-orbit coupling, and constitutes a benchmark of genuine many-body coherence. A physical picture that allows for the analytical study of this nonperturbative effect is provided by a semiclassical approach in Fock space, where coherence arises from interfering amplitudes associated with multiple chaotic mean-field solutions with action degeneracies due to antiunitary symmetries. The analytical predictions resulting from our semiclassical approach are in excellent quantitative agreement with corresponding numerical simulations. The latter, moreover, confirm that the shape of the echo profile is independent of the interaction, while its amplitude and sign universally depend only on the number of flipped spins and the spin-orbit coupling phase.

The structure and dynamics of one-dimensional binary Bose gases forming quantum droplets is studied by solving the corresponding amended Gross-Pitaevskii equation. Two physically different regimes are identified, corresponding to small droplets of an approximately Gaussian shape and large “puddles” with a broad flat-top plateau. Small droplets collide quasielastically, featuring the solitonlike behavior. On the other hand, large colliding droplets may merge or suffer fragmentation, depending on their relative velocity. The frequency of a breathing excited state of droplets, as predicted by the dynamical variational approximation based on the Gaussian ansatz, is found to be in good agreement with numerical results. Finally, the stability diagram for a single droplet with respect to shape excitations with a given wave number is drawn, being consistent with preservation of the Weber number for large droplets.

The many-body dissipative flow induced by a mobile Gaussian impurity harmonically oscillating within a cigar-shaped Bose-Einstein condensate is investigated. For very small and large driving frequencies the superfluid phase is preserved. Dissipation is identified, for intermediate driving frequencies, by the nonzero value of the drag force whose abrupt increase signals the spontaneous downstream emission of an array of gray solitons. After each emission event, typically each of the solitary waves formed decays and splits into two daughter gray solitary waves that are found to be robust propagating in the bosonic background for large evolution times. In particular, a smooth transition toward dissipation is observed, with the critical velocity for solitary wave formation depending on both the characteristics of the obstacle, namely its driving frequency and width as well as on the interaction strength. The variance of a sample of single-shot simulations indicates the fragmented nature of the system; here it is found to increase during evolution for driving frequencies where the coherent structure formation becomes significant. Finally, we demonstrate that for fairly large particle numbers in situ single-shot images directly capture the gray soliton's decay and splitting.

A general mechanism for the loss of conformal invariance is the merger and disappearance of an infrared fixed point and an ultraviolet fixed point of a renormalization group flow. We show explicitly how this mechanism works in the case of identical bosons at unitarity as the spatial dimension $d$ is varied. For $d$ between the critical dimensions $d_1=2.30$ and $d_2=3.76$, there is loss of conformality as evidenced by the Efimov effect in the three-body sector. The $\beta$ function for an appropriate three-body coupling is a quadratic polynomial in that coupling. For $d<d_1$ and for $d>d_2$, the $\beta$ function has two real roots that correspond to infrared and ultraviolet fixed points. As $d$ approaches $d_1$ from below and as $d$ approaches $d_2$ from above, the fixed points merge and disappear into the complex plane. For $d_1<d<d_2$, the $\beta$ function has complex roots and the renormalization group flow for the three-body coupling is a limit cycle.

The dynamics of a few ultracold bosons tunneling from a one-dimensional potential well into an open space is studied. In such a system several decay channels can be distinguished, each corresponding to a different number of bosons escaping simultaneously. We show that as the interparticle interaction strength is changed, the system undergoes transitions between distinct regimes characterized by the dominance of different decay channels. These transitions are reflected in the behavior of the decay rate of the system, which is measurable experimentally. By means of a simple theoretical description, we show that the transitions occur at the points where a new decay channel becomes energetically viable. The results provide insight into the behavior of decaying few-body systems and may have potential interest for experiments.

Examining the Aubry-André-Harper (AAH) model driven by periodic fields, we find a crossover between the localization and delocalization phases. This is different from the sharp phase boundary in the AAH model without drives. On the contrary, the phase boundary in the present model depends on the frequency and amplitude of the driving field. We show numerically the dependence of the phase boundary on the frequency and amplitude and reveal the physics behind the relationship. The effect of aperiodicity of the drive on the localization-delocalization crossover is also investigated by numerical simulations. The results may be useful for engineering novel phases in periodically driven systems.

We consider the energy transfer process between two identical atoms placed inside a perfectly conducting cylindrical waveguide. We first introduce a general analytical expression of the energy transfer amplitude in terms of the electromagnetic Green's tensor; we then evaluate it in the case of a cylindrical waveguide made of a perfect conductor, for which analytical expressions of the Green's tensor exist. We numerically analyze the energy transfer amplitude when the radius of the waveguide is such that the transition frequency of both atoms is below the lower cutoff frequency of the waveguide, so that the resonant photon exchange is strongly suppressed. We consider both cases of atomic dipoles parallel and orthogonal to the axis of the guide. In both cases, we find that the energy transfer is modified by the presence of the waveguide. In the near zone, that is when the atomic separation is smaller than the atomic transition wavelength, the change, with respect to the free-space case, is small for axial dipoles, while it is larger for radial dipoles; it grows when the intermediate region between near and far zone is approached. In the far zone, we find that the energy transfer amplitude is strongly suppressed by the waveguide, becoming virtually zero. A physical interpretation of these results is discussed. Finally, we discuss the resonance interaction energy and force between two identical correlated atoms in the waveguide, one excited and the other in the ground state, prepared in their symmetric or antisymmetric superposition.

We consider regimes of spontaneous parametric down-conversion, both noncollinear and nondegenerate in frequencies. Parameters characterizing degrees of noncollinearity and of nondegeneracy are defined, and they are shown to be not independent of each other. At a given degree of nondegeneracy the emitted photons are shown to propagate along two different cones, the opening angles of which are determined by the degree of nondegeneracy. Based on this, the degree of nondegeneracy can be controlled by means of the angular selection of photons, e.g., with the help of appropriately installed slits. For such selected photons their wave functions are found depending on two frequencies or on two temporal variables. Interference effects arising in such states are tested by analysis of the Hong-Ou-Mandel–type scheme with a varying delay time in one of two channels and with photons from two channels sent to the beamsplitter. The temporal pictures arising after the beamsplitter are found to demonstrate extremely strong interference, exhibiting itself in formation of finite-size temporal combs filled with quantum beats. Parameters of combs depend on the degree of nondegeneracy, and the physical reasons for this dependence are clarified.

We consider the reduced dynamics in a bipartite quantum system (consisting of a central system and an intermediate environment) coupled to a heat bath at finite temperature. To describe this situation, in the simplest possible—yet physically meaningful—way, we introduce the “depolarizing heat bath” as a minimal dissipation model. We conjecture that, at sufficiently strong dissipation, any other dissipation model implemented in the form of a Markovian quantum master equation will yield the same reduced dynamics of the central system as the minimal model. To support this conjecture, we study a two-level system coupled to an oscillator mode. For the coupling between the two parts, we consider the Jaynes-Cummings or a dephasing coupling, while the coupling to the heat bath is modeled by the quantum optical or the Caldeira-Leggett master equation (neglecting any direct coupling between central system and heat bath). We then provide ample numerical evidence for both model independence and accuracy of the depolarizing heat bath model. Alongside our study, we investigate different regimes, where the strong-coupling condition leads to coherence and/or population stabilization.

We study transmission stabilization against radiation emission and enhancement of transmission quality in soliton-based nonlinear optical waveguides with weak linear gain-loss, cubic loss, and delayed Raman response. We show by numerical simulations with perturbed nonlinear Schrödinger propagation models that transmission quality in waveguides with frequency-independent linear gain and cubic loss is not improved by the presence of delayed Raman response due to the lack of an efficient mechanism for suppression of radiation emission. In contrast, we find that the presence of delayed Raman response leads to significant enhancement of transmission quality in waveguides with frequency-dependent linear gain-loss and cubic loss. Enhancement of transmission quality in the latter waveguides is enabled by the separation of the soliton's spectrum from the radiation's spectrum due to the Raman-induced self-frequency shift and by efficient suppression of radiation emission due to the frequency-dependent linear gain-loss. Further numerical simulations demonstrate that the enhancement of transmission quality in waveguides with frequency-dependent linear gain-loss, cubic loss, and delayed Raman response is similar to transmission quality enhancement in waveguides with linear gain, cubic loss, and guiding filters with a varying central frequency. Thus, our study demonstrates a general mechanism for stabilizing soliton transmission, which is based on the interplay between frequency-dependent linear gain-loss and perturbation-induced shifting of the soliton frequency.