We show that the maximum transmission distance of continuous-variable quantum key distribution in presence of a Gaussian noisy lossy channel can be arbitrarily increased using a heralded noiseless linear amplifier. We explicitly consider a protocol using amplitude- and phase-modulated coherent states with reverse reconciliation. Assuming that the secret key rate drops to zero for a line transmittance $T_{\lim }$, we find that a noiseless amplifier with amplitude gain $g$ can improve this value to $T_{\lim }/g^2$, corresponding to an increase in distance proportional to $\log g$.

Starting from the Weyl gauge formulation of quantum electrodynamics (QED), the formalism of quantum-mechanical gauge fixing is extended using techniques from nonrelativistic QED. This involves expressing the redundant gauge degrees of freedom through an arbitrary functional of the gauge-invariant transverse degrees of freedom. Particular choices of functional can be made to yield the Coulomb gauge and Poincaré gauge representations. The Hamiltonian we derive therefore serves as a good starting point for the description of atoms and molecules by means of a relativistic Dirac field. We discuss important implications for the ontology of noncovariant canonical QED due to the gauge freedom that remains present in our formulation.

Quantum measurements provide a trove of information about a quantum system or process without solution of the Schrödnger equation, and in principle, the associated density matrix is a function of these measurements. Inversion of the measurements can produce an estimate of the density matrix, but this estimate may be unphysical, especially when the measurements are noisy or incomplete. We develop a general approach based on semidefinite programming [D. A. Mazziotti, Phys. Rev. Lett. 106, 083001 (2011)] for reconstructing the density matrix from quantum measurements which leads naturally to nonnegative solutions, a critical attribute of physically realistic solutions. We discuss the use of this methodology for reconstructing $p$-particle reduced density matrices ($p$-RDMs) of $N$-particle systems where additional semidefinite constraints, known as $N$-representability conditions, are essential because they ensure that the $p$-RDM represents an $N$-particle system. Special attention is given to the $N$-representability conditions for the experimentally important cases where $p=1$ or 2. We apply the methodology to reconstructing the time-dependent quantum process of exciton transfer in a photosynthetic light-harvesting complex.

Femtosecond-induced resonance-enhanced multiphoton-ionization photoelectron spectroscopy (REMPI-PS) suffers from poor spectral resolution due to the large laser spectral bandwidth. In this paper, we present a scheme to achieve high-resolution REMPI-PS in the potassium atom by shaping the ultrashort femtosecond laser pulse. Our results show that the REMPI-PS bandwidth can be narrowed by several tens of times with a cubic spectral phase modulation, and thus high-resolution REMPI-PS and the fine structure of the energy-level diagram for multiple excited states can be obtained in spite of the broadband femtosecond laser pulse. Furthermore, we explain the physical control mechanism of the narrowband REMPI-PS by considering the two-photon power spectrum.

We propose and demonstrate an efficient scheme for steering the electron localization of hydrogen molecules and their isotopes. Our scheme is based on the idea of subcycle waveform shaping by synthesizing coherent multicycle IR pulses of different wavelengths. This scheme leads to a good balance between the control of electronic and molecular motions. The results of a quantum model simulation indicate a substantial enhancement of the electron localization asymmetry compared with that of a few-cycle one-color pulse. Sixty-eight percent and $89\%$ of the electrons in the dissociating fragments can be localized to one nucleus for ${{\text{H}}_2}^{+}$ and ${\text{H}}_2$, respectively.

The cooling rate for cavity-mediated laser cooling scales as the Lamb-Dicke parameter $\eta$ squared. A proper analysis of the cooling process hence needs to take terms up to ${\eta }^2$ in the system dynamics into account. In this paper, we present such an analysis for a standard scenario of cavity-mediated laser cooling with $\eta \ll 1$. Our results confirm that there are many similarities between ordinary and cavity-mediated laser cooling. However, for a weakly confined particle inside a strongly coupled cavity, which is the most interesting case for the cooling of molecules, numerical results indicate that more detailed calculations are needed to model the cooling process accurately.

Quantum control tasks are classified either as classical-like or as quantum requiring interference of pathways. We study the generation of interference pathways and relate them to the fidelity of the control target at a fixed time for various tasks. The model drift Hamiltonian studied is the two-dimensional Henon-Heiles (HH) potential. This system shows regular classical dynamics for low energies and chaotic dynamics for higher energies. A control operator supported by the whole momentum space and therefore connecting the entire Hilbert phase space is a random spiky potential. The other extreme is a smooth control potential. Intermediate cases are obtained by filtering the random spiky potential in momentum space. The fidelity of achieving a control task was related to the connectivity in phase space of the control operators. Typical quantum tasks such as generating a superposition of generalized coherent states rely on interfering pathways. For these cases the nonlinearity in the drift or control Hamiltonian is a necessary requirement for creating interferences. Control over rapidly diverging components of the wave function is achieved by the use of highly nonlocal control operators. Quantum control under chaotic drift was found to give a better yield than control under regular dynamics for such cases. For classical tasks we study the transformation of an initial generalized coherent state to another one. The best fidelity is obtained for regular or harmonic regions of the potential and smooth control operators. The approach to the classical limit is checked by decreasing the effective value of $\hslash$. Control under both quantum and classical tasks suffered from the decrease of $\hslash$ and the approach to classical proximity. Classical control tasks which rely heavily on maintaining a generalized coherent state throughout the evolution were found to be dysfunctional and lead to a completely uncontrolled situation once the classical chaos starts to appear.

We investigate the strong-coupling limit of a three-component Fermi mixture in an optical lattice with attractive interactions. In this limit bound states (trions) of the three components are formed. We study the effective Hamiltonian for these composite fermions and show that it is asymptotically equivalent at the leading order to an antiferromagnetic Ising model. By using Monte Carlo simulations, we investigate the spatial arrangement of the trions in this regime and the formation of a trionic density wave, both in a homogeneous lattice and in the presence of an additional harmonic confinement. Depending on the strength of the confinement and on the temperature, we found several scenarios for the trionic distribution, including the coexistence of disordered trions with a density wave and band insulator phases. Our results show that, due to a proximity effect, staggered density modulations are induced in regions of the trap where they would not otherwise be present according to the local density approximation.

We show that a moving obstacle, in the form of an elongated paddle, can create vortices that are dispersed or induce clusters of like-signed vortices in two-dimensional (2D) Bose-Einstein condensates. We propose statistical measures of clustering based on Ripley's $K$ function which are suitable to the small size and small number of vortices in atomic condensates, which lack the huge number of length scales excited in larger classical and quantum turbulent fluid systems. The evolution and decay of clustering is analyzed using these measures. Experimentally it should prove possible to create such an obstacle by a laser beam and a moving optical mask. The theoretical techniques we present are accessible to experimentalists and extend the current methods available to induce 2D quantum turbulence in Bose-Einstein condensates.

We examine spatial localization and dynamical stability of Bose-Einstein condensates of exciton polaritons in microcavities under the condition of off-resonant spatially inhomogeneous optical pumping both with and without a harmonic trapping potential. We employ the open-dissipative Gross-Pitaevskii model for describing an incoherently pumped polariton condensate coupled to an exciton reservoir, and reveal that spatial localization of the steady-state condensate occurs due to the effective self-trapping created by the polariton flows supported by the spatially inhomogeneous pump, regardless of the presence of the external potential. A ground state of the polariton condensate with repulsive interactions between the quasiparticles represents a dynamically stable bright dissipative soliton. We also investigate the conditions for sustaining spatially localized structures with nonzero angular momentum in the form of single-charge vortices.

It is a well-established fact that statistical properties of energy-level spectra are the most efficient tool to characterize nonintegrable quantum systems. The statistical behavior of different systems such as complex atoms, atomic nuclei, two-dimensional Hamiltonians, quantum billiards, and noninteracting many bosons has been studied. The study of statistical properties and spectral fluctuations in interacting many-boson systems has developed interest in this direction. We are especially interested in weakly interacting trapped bosons in the context of Bose-Einstein condensation (BEC) as the energy spectrum shows a transition from a collective nature to a single-particle nature with an increase in the number of levels. However this has received less attention as it is believed that the system may exhibit Poisson-like fluctuations due to the existence of an external harmonic trap. Here we compute numerically the energy levels of the zero-temperature many-boson systems which are weakly interacting through the van der Waals potential and are confined in the three-dimensional harmonic potential. We study the nearest-neighbor spacing distribution and the spectral rigidity by unfolding the spectrum. It is found that an increase in the number of energy levels for repulsive BEC induces a transition from a Wigner-like form displaying level repulsion to the Poisson distribution for $P\left(s\right)$. It does not follow the Gaussian orthogonal ensemble prediction. For repulsive interaction, the lower levels are correlated and manifest level-repulsion. For intermediate levels $P\left(s\right)$ shows mixed statistics, which clearly signifies the existence of two energy scales: external trap and interatomic interaction, whereas for very high levels the trapping potential dominates, generating a Poisson distribution. Comparison with mean-field results for lower levels are also presented. For attractive BEC near the critical point we observe the Shnirelman-like peak near $s=0$, which signifies the presence of a large number of quasidegenerate states.

We develop a model for parametric amplification, based on a density matrix approach, which naturally accounts for the peculiarities arising for matter waves: significant depletion and explicit time dependence of the source state population, long interaction times, and spatial dynamics of the amplified modes. We apply our model to explain the details in an experimental study on twin-atom beam emission from a one-dimensional degenerate Bose gas.

We propose an experimental scheme in which two orthogonally polarized thermal light beams with antisymmetrical wavefronts are overlapped. The experimental results demonstrate that this setup can focus the beam in two-photon and multiphoton correlation measurements. The focused “two-photon” spot possesses subwavelength resolution, surpassing the classical diffraction limit. Since the experimental setup consists of only two right-angle-mirror devices without the help of lenses, the two-photon focusing effect does not apparently rely on the beam focusing. Physically, the phenomenon signifies that the photon bunching can be localized within a very small region through two-photon interference in contrast to the conventional Hanbury Brown–Twiss effect of thermal light. In the higher-order intensity correlation measurement, the multiphoton bunching can be limited within a very small central region while the background is greatly suppressed.

The quantum ground-state and excitation properties of two independent chains of pseudospins (two-level systems) interacting with the same bosonic field are theoretically investigated. Each chain is coupled to a different quadrature of the field, leading to two independent symmetry breakings for increasing values of the two collective spin-boson interaction constants ${\Omega }_C$ and ${\Omega }_I$. A phase diagram is provided in the plane (${\Omega }_C$,${\Omega }_I$), with four phases that can be characterized by the complex bosonic coherence of the ground states and can be manipulated via geometric Berry effects. In particular, when ${\Omega }_C$ and ${\Omega }_I$ are both larger than two critical values, the fundamental subspace has a fourfold degeneracy. Finite-size properties are shown for both critical and ultrastrong values of ${\Omega }_C$ and ${\Omega }_I$. Possible implementations in superconducting quantum circuits are detailed.

We present a quantum memory protocol that allows us to store light in ensembles of two-level atoms, e.g., rare-earth-metal ions doped into a crystal, by modulating the refractive index of the host medium of the atoms linearly in time. We show that under certain conditions the resulting dynamics is equivalent to that underlying the gradient echo memory protocol, which relies on a spatial gradient of the atomic resonance frequencies. We discuss the prospects for an experimental implementation.

Reverse propagation is a numeric technique that makes it possible to obtain arbitrarily shaped pulses after propagation through a fiber in the nonlinear regime. We apply it to achieve selective two-photon excitation of dyes that have overlapping absorption spectra with pulses transported through the fiber. By comparing both contrast and signal level it is shown that phase and amplitude shaped pulses generated using reverse propagation are superior to pulses with antisymmetric phase despite loss caused by amplitude shaping.

Filamentation-assisted spatiotemporal dynamics of ultrashort laser pulses in the regime of extreme light powers is shown to enable self-compression of subpetawatt laser pulses to relativistic field intensities and subcycle pulse widths. Our supercomputer simulations demonstrate compression of 6-J, 30-fs laser pulses at a central wavelength of 800 nm to 1.3-fs sub-100-TW broadband field waveforms and reveal the generation of relativistic-intensity subfemtosecond field transients as a result of such a pulse evolution scenario, with multiple filamentation avoided due to low gas pressures and the balance between Kerr and ionization nonlinearities steered toward optimal pulse compression due to the depletion of outer-shell ionization in a high-intensity laser field.

A criterion for strong coupling between two quantum emitters and a single resonant light mode in a cavity is presented. The criterion takes into account the escape of cavity photons and the spontaneous emission of the emitters, which are modeled as two-level systems. By using such a criterion, the dissipative Tavis-Cummings ladder of states is constructed, and it is shown that the inclusion of one more emitter with respect to the Jaynes-Cummings (single emitter) case increases the effective parameter region in which $n\text{th}$-order Rabi splitting is observed.

Recently, Qi and Hou [Phys. Rev. A 85, 022334 (2012)] provided optimal entanglement witnesses without the spanning property. These witnesses are associated with indecomposable positive linear maps, but whether partial transposes of these witnesses are also optimal has not been evaluated. We show that partial transposes of these entanglement witnesses have the spanning property and that these witnesses are indeed optimal witnesses detecting positive-partial- transposed entangled states (nondecomposable optimal entanglement witnesses).

The combination of adiabatic rapid passage and multiphoton Bragg diffraction (ARPMB pulses) to efficiently transfer many photon recoils of momentum ($\hslash k$) to cold-atom clouds is theoretically and experimentally investigated. This method is insensitive to perturbations of the pulse intensity or detuning. In particular, the theoretically calculated velocity acceptance can be up to $80\%$ of one recoil velocity $v_r$, the theoretical maximum in Bragg diffraction. We experimentally demonstrate ARPMB pulses with transfer efficiency of 99.7$\%$ per $\hslash k$ using $10\hslash k$ pulses, limited by spontaneous emission losses, and Mach-Zehnder interferometers with $80\%$ contrast.