The interaction blockade phenomenon isolates the motion of a single quantum particle within a multiparticle system, in particular for coherent oscillations in and out of a region affected by the blockade mechanism. For identical quantum particles with Bose statistics, the presence of the other particles is still felt by a bosonic stimulation factor $\sqrt{N}$ that speeds up the coherent oscillations, where $N$ is the number of bosons. Here we propose an experiment to observe this enhancement factor with a small number of bosonic atoms. The proposed protocol realizes an asymmetric double-well potential with multiple optical tweezer laser beams. The ability to adjust bias independently of the coherent coupling between the wells allows the potential to be loaded with different particle numbers while maintaining the resonance condition needed for coherent oscillations. Numerical simulations with up to three bosons in a realistic potential generated by three optical tweezers predict that the relevant avoided level crossing can be probed and the expected bosonic enhancement factor observed.

We address the time evolution of two- and three-dimensional nonrelativistic Gaussian wave packets in the presence of a weak external potential of arbitrary functional form. The focus of our study is the phenomenon of rotation of a Gaussian wave packet around its center of mass, as quantified by mean angular momentum computed relative to the wave-packet center. Using a semiclassical approximation of the eikonal type, we derive an explicit formula for a time-dependent change of mean angular momentum of a wave packet induced by its interaction with a weak external potential. As an example, we apply our analytical approach to the scenario of a two-dimensional quantum particle crossing a tilted ridge potential barrier. In particular, we demonstrate that the initial orientation of the particle wave packet determines the sense of its rotation, and report a good agreement between analytical and numerical results.

We explore the impact of dimensionality on the scattering of a small bosonic ensemble in an elongated harmonic trap off a centered repulsive barrier, thereby taking particle correlations into account. The loss of coherence as well as the oscillation of the center of mass are studied and we analyze the influence of both particle and spatial correlations. Two different mechanisms of coherence losses in dependence of the aspect ratio are found. For small aspect ratios, loss of coherence between the region close to the barrier and outer regions occurs, due to spatial correlations, and for large aspect ratios, incoherence between the two density fragments of the left and right side of the barrier arises due to particle correlations. Apart from the decay of the center-of-mass motion induced by the reflection and transmission, further effects due to the particle and spatial correlations are explored. For tight transversal traps, the amplitude of the center-of-mass oscillation experiences a weaker damping, which can be traced back to the population of a second natural orbital, and for a weaker transversal confinement, we detect a strong decay due to the possibility of transferring energy to transversal excited modes. These effects are enhanced if the aspect ratio is integer valued.

With Maxwell-Bloch equations how the superradiance can lead to amplification and gain at a frequency much larger than the pumping frequency has been shown. This remarkable effect has been examined in terms of a simpler model involving two coupled oscillators, with one of them parametrically driven. We show that this coupled-oscillator model has a hidden parity-time ($\mathcal{PT}$) symmetry for quantum amplification by superradiant emission of radiation (QASER); we thus bring $\mathcal{PT}$ symmetry to the realm of parametrically coupled resonators. Moreover, we find that the QASER gain arises from the broken-$\mathcal{PT}$-symmetry phase. We then quantize the simplified version of QASER using quantum Langevin equations. The quantum description enables us to understand how the system starts from quantum fluctuations.

The damped driven nonlinear Schrödinger equation (NLSE) has been used to understand a range of physical phenomena in diverse systems. Studying this equation in the context of optical hyperparametric oscillators in anomalous-dispersion dissipative cavities, where NLSE is usually referred to as the Lugiato-Lefever equation, we are led to a reduced nonlinear oscillator model that uncovers the essence of the spontaneous creation of sharply peaked pulses in optical resonators. We identify attracting solutions for this model, which correspond to stable cavity solitons and Turing patterns, and study their degree of stability. The reduced model embodies the fundamental connection between mode synchronization and spatiotemporal pattern formation and represents a class of self-synchronization processes in which coupling between nonlinear oscillators is governed by energy and momentum conservation.

We present an unusual example of truly long-range propagation of high-power laser pulses through strong atmospheric turbulence. A form of nonlinear self-channeling is achieved when the laser power is close to the self-focusing power of air and the transverse dimensions of the pulse are smaller than the coherence diameter of turbulence. In this mode, nonlinear self-focusing counteracts diffraction, and turbulence-induced spreading is greatly reduced. Furthermore, the laser intensity is below the ionization threshold so that multiphoton absorption and plasma defocusing are avoided. Simulations show that the pulse can propagate many Rayleigh lengths (several kilometers) while maintaining a high intensity. In the presence of aerosols, or other extinction mechanisms that deplete laser energy, the pulse can be chirped to maintain the channeling.

Backflow is the phenomenon that the probability current of a quantum particle on the line can flow in the direction opposite to its momentum. In this paper, previous investigations of backflow, pertaining to interaction-free dynamics or purely kinematical aspects, are extended to scattering situations in short-range potentials. It is shown that backflow is a universal quantum effect which exists in any such potential, and is always of bounded spatial extent in a specific sense. The effects of reflection and transmission processes on backflow are investigated, both analytically for general potentials and numerically in various concrete examples.

In this paper, we prove that $K_G\left(3\right)<K_G\left(4\right)$, where $K_G\left(d\right)$ denotes the Grothendieck constant of order $d$. To this end, we use a branch-and-bound algorithm commonly used in the solution of NP-hard problems. It has recently been proven that $K_G\left(3\right)\le 1.4644$. Here we prove that $K_G\left(4\right)\ge 1.4841$, which has implications for device-independent witnessing dimensions greater than two. Furthermore, the algorithm with some modifications may find applications in various black-box quantum information tasks with large number of inputs and outputs.

Employing quadratic fermionic and bosonic Hamiltonians for collective and internal subsystems with a linear rotating-wave-approximation coupling, we studied the role of heat-bath statistics on the dynamics of the collective motion. The master equations for the collective occupation number derived directly from the quadratic Hamiltonians and within the Non-Markovian Langevin approach are discussed and their solutions are obtained. Because of the different nature of the heat-bath statistics, the path to equilibrium or the relaxation time is affected as shown in the numerical calculations.

We study the fluctuations of the work performed on a driven quantum system, defined as the difference between subsequent measurements of energy eigenvalues. These work fluctuations are governed by statistical theorems with similar expressions in classical and quantum physics. We show that we can distinguish quantum and classical work fluctuations, as the latter can be described by a macrorealistic theory and hence obey Leggett-Garg inequalities. We show that these inequalities are violated by quantum processes in a driven two-level system and in a harmonic oscillator subject to a squeezing transformation.

It has been recently demonstrated that a singlet-triplet spin qubit in semiconductor double quantum dots can be controlled by changing the height of the potential barrier between the two dots (“barrier control”), which has led to a considerable reduction of charge noises as compared with the traditional tilt control method. In this paper we show, through a molecular-orbital-theoretic calculation of double quantum dots influenced by a charged impurity, that the relative charge noise for a system under the barrier control not only is smaller than that for the tilt control but actually decreases as a function of an increasing exchange interaction. This is understood as a combined consequence of the greatly suppressed detuning noise when the two dots are symmetrically operated, as well as an enhancement of the interdot hopping energy of an electron when the barrier is lowered which in turn reduces the relative charge noise at large exchange interaction values. We have also studied the response of the qubit to charged impurities at different locations and found that the improvement of barrier control is least for impurities equidistant from the two dots due to the small detuning noise they cause but is otherwise significant along other directions.

A noiseless linear amplifier (NLA) adds no noise to the signals it processes, which works only in a probabilistic way. It can be realized approximately with either a physical implementation that truncates the working space of the NLA on a photon-number basis or a measurement-based implementation that realizes the truncation virtually by a bounded postselection filter. To examine the relationship between these two approximate NLAs, we characterize in detail the measurement-based NLA and compare it with its physical counterpart in terms of their abilities to preserve the state Gaussianity and their probability of success. The link between these amplifiers is further clarified by integrating them into a measure-and-prepare setup. We stress the equivalence between the physical and the measurement-based approaches holds only when the effective parameters, the amplification gain, the cutoff, and the amplitude of the input state, are taken into account. Finally, we construct a 1-to-infinity cloner using the two amplifiers and show that a fidelity surpassing the no-cloning limit is achievable with the measurement-based NLA.

We calculate the $g$ factor of the $6s6p{}^{3}P_0$ state of 199 and 201 mercury isotopes using a relativistic high-precision all-order method that combines the configuration interaction and the coupled-cluster approaches. Our values $g\left({}^{199}\mathrm{Hg}\right)=-0.9485\left(49\right)\times {10}^{-3}$ and $g\left({}^{201}\mathrm{Hg}\right)=0.3504\left(18\right)\times {10}^{-3}$ are in agreement with the experimental measurements within the 0.5% theoretical uncertainty. We also calculate the hyperfine quenching rate of the $6s6p{}^3{P}_0$ state in ${}^{199}\mathrm{Hg}$ and ${}^{201}\mathrm{Hg}$ and determine its lifetime to be 1.3 and 1.9 s, respectively.

The $Z$-vector method in the relativistic coupled-cluster framework is used to calculate the magnetic hyperfine structure constant ($A_J$) of alkali metals and singly charged alkaline earth metals in their ground state electronic configuration. The $Z$-vector results are in very good agreement with the experiment. The $A_J$ values of Li, Na, K, Rb, Cs, ${\mathrm{Be}}^{+}$, ${\mathrm{Mg}}^{+}$, ${\mathrm{Ca}}^{+}$, and ${\mathrm{Sr}}^{+}$ obtained in the $Z$-vector method are compared with the extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The same basis and cutoff are used for the comparison purpose. The comparison shows that the $Z$-vector method with the single and double approximation can produce a more precise wave function in the nuclear region than the ECC method.

We have verified a mechanism for Raman excitation of atoms through continuum levels previously obtained by quantum optimal control using the multiconfigurational time-dependent Hartree-Fock (MCTDHF) method. For the optimal control, which requires running multiple propagations to determine the optimal pulse sequence, we used the computationally inexpensive time-dependent configuration interaction singles (TDCIS) method. TDCIS captures all of the necessary correlation of the desired processes but assumes that ionization pathways reached via double excitations are not present. MCTDHF includes these pathways and all multiparticle correlations in a set of time-dependent orbitals. The mechanism that was determined to be optimal in the Raman excitation of the Ne $1s^{2}2s^{2}2p^{5}3p^1$ valence state via the metastable $1s^{2}2s^{1}2p^{6}3p^1$ resonance state involves a sequential resonance-valence excitation. First, a long pump pulse excites the core-hole state, and then a shorter Stokes pulse transfers the population to the valence state. This process represents the first step in a multidimensional x-ray spectroscopy scheme that will provide a local probe of valence electronic correlations. Although at the optimal pulse intensities at the TDCIS level of theory the MCTDHF method predicts multiple ionization or excitation ionization of the atom, at slightly lower intensities (reduced by a factor of about 4) the TDCIS mechanism is shown to hold qualitatively. Quantitatively, the MCTDHF populations are reduced from the TDCIS calculations by a factor of 4.

The emphasis of this work is on the computation of physical properties as well as of the wave function of interacting bosons in a trap potential. Many-body perturbation theory is employed to study the leading term of these quantities for finite numbers of bosons, and exact solutions are aimed at in the infinite-particle limit. As discussed before, a suitable starting point is the second-quantized Hamiltonian represented in the basis of destruction and creation operators of its own mean-field potential. This choice leads to expressions for the perturbation terms of all quantities which exhibit a very weak dependence on the particle number. Importantly, when applying ideas similar to Bogoliubov's, the Hamiltonian can be reduced in the infinite-particle limit to a much simplified form which is a priori particle-number conserving. The resulting phonon Hamiltonian is diagonalizable by a linear transformation for which an explicit eigenvalue equation is given. Physical properties can be expressed explicitly by elements of this transformation, and of particular relevance is that the particle-number-conserving wave functions of the original many-boson system can be reconstructed using recursion relations. The reconstruction of the particle-conserving wave function from the phonon Hamiltonian can also be used to assess when the infinite-particle limit is reached in practice for finite trapped condensates. Two applications are discussed in detail. For one of them, an exact solution is known which is found, in the infinite-particle limit, to exactly coincide with that of the phonon Hamiltonian. In both examples expressions for the properties are given in closed form. The physics behind the phonon Hamiltonian and its physical properties is discussed.

Many-body entangled states are key elements in quantum information science and quantum metrology. One important problem in establishing a high degree of many-body entanglement using optical techniques is the leakage of the system information via the light that creates such entanglement. We propose an all-optical interference-based approach to erase this information. Unwanted atom-light entanglement can be removed by destructive interference of three or more successive atom-light interactions, leaving behind only atom-atom entanglement. This quantum erasure protocol allows implementation of spin squeezing with Heisenberg scaling using coherent light and a cold or warm atomic ensemble. Calculations show that a significant improvement in the squeezing exceeding 10 dB is obtained compared to previous methods, and substantial spin squeezing is attainable even under moderate experimental conditions. Our method enables the efficient creation of many-body entangled states with simple setups and, thus, is promising for advancing technologies in quantum metrology and quantum information processing.

Taking the decoherence into account, we investigate nonclassical features of the optical Schrödinger cat states in one-mode and two-coupled-modes systems with two-photon driving. In the one-mode system, the relationship between the Schrödinger cat states and the system parameters is derived. We observe that in the presence of single-photon decay the steady states would be a mixture of Schrödinger cat states. The dynamics and steady states of such a cat versus single-photon decay are examined. In the two-coupled-modes cases with linear and nonlinear couplings, the dynamics of entanglement and mutual information are examined with two different initial states and single-photon decay. Compared to the linear coupling case, more complicated structure appears in the Wigner function in the nonlinear coupling case. The joint quadrature distributions are also explored. Such nonclassical states can be used not only in exploring the boundary between the classical and the quantum worlds but also in quantum metrology and quantum information processing.

We study theoretically the concept of homogenization in optics using an ensemble of randomly distributed resonant stationary atoms with density $\rho$. The ensemble is dense enough for the usual condition for homogenization, viz. $\rho {\lambda }^3\gg 1$, to be reached. Introducing the coherent and incoherent scattered powers, we define two criteria to define the homogenization regime. We find that when the excitation field is tuned in a broad frequency range around the resonance, neither of the criteria for homogenization is fulfilled, meaning that the condition $\rho {\lambda }^3\gg 1$ is not sufficient to characterize the homogenized regime around the atomic resonance. We interpret these results as a consequence of the light-induced dipole-dipole interactions between the atoms, which implies a description of scattering in terms of collective modes rather than as a sequence of individual scattering events. Finally, we show that, although homogenization can never be reached for a dense ensemble of randomly positioned laser-cooled atoms around resonance, it becomes possible if one introduces spatial correlations in the positions of the atoms or nonradiative losses, such as would be the case for organic molecules or quantum dots coupled to a phonon bath.

We consider the evolution of fiber-optic solitons in the presence of loss. Localized power reduction can be cast into a well-known form for which changes of all parameters are known explicitly. We proceed to a sequence of such perturbations with the same total loss, so that still all parameters are known, and eventually take the limit to infinitely many steps. This establishes the connection with distributed loss, and in the limit of vanishing loss reproduces the known results from perturbation theory. Outside this adiabatic limit the mechanism becomes clear that causes deviations: interference between solitons and radiation upsets the balance of dispersive and nonlinear effects characteristic of solitons; as one consequence the soliton continually sheds energy, which goes into radiation. We derive an expression for the radiation production rate in a lossy fiber, and predict quantitatively the distance until the soliton finally decays. Our approach provides quantitative results for fibers with loss small or strong, localized or distributed, and numerical results confirm predictions. It can be generalized to gain rather than loss.