A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative $N$-qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.

Maximally entangled states—a resource for quantum information processing—can only be shared through noiseless quantum channels, whereas in practice channels are noisy. Here we ask: Given a noisy quantum channel, what is the maximum attainable purity (measured by singlet fraction) of shared entanglement for single channel use and local trace preserving operations? We find an exact formula of the maximum singlet fraction attainable for a qubit channel and give an explicit protocol to achieve the optimal value. The protocol distinguishes between unital and nonunital channels and requires no local postprocessing. In particular, the optimal singlet fraction is achieved by transmitting part of an appropriate pure entangled state, which is maximally entangled if and only if the channel is unital. A linear function of the optimal singlet fraction is also shown to be an upper bound on the distillable entanglement of the mixed state dual to the channel.

We analyze and evaluate perfect controlled teleportation via three-qubit entangled channels from the point of view of the controller. The key idea in controlled teleportation is that the teleportation is performed only with the participation of the controller. We calculate a quantitative measure of the controller's power and establish a lower bound on the control power required for controlled teleportation. We show that the maximally entangled Greenberger-Horne-Zeilinger state is a suitable channel for controlled teleportation of arbitrary single qubits—the controller's power meets the bound and the teleportation fidelity without the controller's permission is no better than the fidelity of a classical channel. We also construct partially entangled channels that exceed the bound for controlled teleportation of a restricted set of states called the equatorial states. We calculate the minimum entanglement required in these channels to exceed the bound. Moreover, we find that in these restricted controlled teleportation schemes, the partially entangled channels can outperform maximally entangled channels with respect to the controller's power. Our results provide an alternative perspective on controlled teleportation schemes and are of practical interest since we propose useful partially entangled channels.

The energy levels of the first few low-lying states of carbon in intense magnetic fields upwards of $\approx {10}^7$ T are calculated in this study. We extend our previously employed pseudospectral approach for calculating the eigenstates of the carbon atom. We report data for the ground state and a low-lying state that are in good agreement with findings elsewhere, as well as additional data for ten other states of the carbon atom. It is seen that these latter states also become strongly bound with increasing magnetic field strengths. The data presented in this study are relevant for astrophysical applications, such as magnetized white dwarf and neutron star spectral analysis as well as opacity calculations and absorption features, including in the context of material accreting onto the surfaces of these compact objects.

We present a first principles description of the interaction of two ground-state scandium atoms. Scandium has a ${{}^{2}D}_g$ ground state. Thirty molecular states correlate to the lowest dissociation limit of the dimer. In the short range, potential energy curves are calculated using second-order $n$-electron valence state perturbation theory. The first-order long-range interaction is calculated at the complete active space self-consistent field level. We determine the second-order long-range dispersion interaction from atomic dynamic polarizabilities at imaginary frequencies. These polarizabilities are calculated using time-dependent density functional theory. We merge the short-range approach with the long-range model to obtain a physical description of the 30 potential energy curves correlating to the ${{}^{2}D}_g+{{}^{2}D}_g$ limit. Diabatic potentials are presented that can be used in quantum scattering calculations, in order to study Zeeman relaxation of ultracold scandium atoms.

The binary collision dynamics of ${}^2{D}_{g,3/2}$ ground state scandium atoms is studied from first principles. We employ 30 coupled diabatic ab initio potentials in a coupled-channels study of the scattering dynamics of cold and ultracold scandium atoms in external magnetic fields. Due to the long-ranged magnetic dipolar interaction, the field dependence of the cross section does not follow the threshold laws derived by Volpi and Bohn [Phys. Rev. A 65, 052712 (2002)]. In the field-free case, the near-threshold cross section is independent of the collision energy, and hence the cross section does not follow the well-established Wigner threshold laws. The observed threshold behavior is explained in the Born approximation. For energies above $1\mu \mathrm{K}$, inelastic collisions are driven by the anisotropic nonrelativistic electronic interaction. For energies below $100\mu \mathrm{K}$, the ratio of elastic-to-inelastic collisions is likely to be favorable for evaporative cooling. Both anisotropy in the long-range interaction and in the short-range potential contribute to large cross sections for inelastic collisions at higher energies and lead to a small ratio of elastic-to-inelastic collisions. This is in agreement with the large rates for Zeeman relaxation of submerged-shell atoms observed experimentally. The effect of the uncertainty in the ab initio potential is sampled by scaling the reduced mass and is found to have little influence on the conclusions drawn from this work.

We study arrays of plasmonic nanoparticles combined with quantum emitters, quantum plasmonic lattices, as a platform for room-temperature studies of quantum many-body physics. We outline a theory to describe surface plasmon-polariton distributions when they are coupled to externally pumped molecules. The possibility of tailoring the dispersion in plasmonic lattices allows realization of a variety of distributions, including the Bose-Einstein distribution as in photon condensation [Klaers et al., Nature (London) 468, 545 (2010)]. We show that the presence of losses can relax some of the standard dimensionality restrictions for condensation.

We present a description of a strongly driven multimode optomechanical system that shows the emergence of cooperative effects usually known from systems of atom-light interaction. Our calculations show that under application of a coherent pump field the system's response can be switched from a superradiant regime to a collective gain regime by varying the frequency detuning of the pump. In the superradiant regime, enhanced optical cooling of a single vibrational mode is possible, whereas the collective gain regime would potentially enable one to achieve almost thresholdless phonon laser action. The threshold pumping power scales as $1/N$.

We adopt Ramsey's method of separated oscillatory fields to study coherences of the mechanical system in an optomechanical resonator. The high-resolution Ramsey fringes are observed in the emission optical field, when two pulses separated in time are applied. We develop a theory to describe the transient optomechanical behavior underlying the Ramsey fringes. We also perform the experimental demonstration using a silica microresonator. The method is versatile and can be adopted for different types of mechanical resonators and electromechanical resonators.

Recent years have witnessed significant interest in nanoscale physical systems, such as nanoelectromechanical and optomechanical systems, which can exhibit distinct collective dynamical behaviors, such as synchronization. As a parameter of the system changes, transition from one type of emerging collective behavior to another can occur. But what are the quantum manifestations of such a transition? We investigate a system of two optically coupled optomechanical cavities and uncover the phenomenon of transition from in-phase to antiphase synchronization. Quantum mechanically, we find that, associated with the classical transition, the entanglement measures between the various optical and mechanical degrees of freedom in the two cavities exhibit a change characteristic of second-order phase transition. These phenomena can be tested experimentally.

We report on a joint theoretical and experimental study of an integrated photonic device consisting of a single-mode waveguide vertically coupled to a disk-shaped microresonator. Starting from the general theory of open systems, we show how the presence of a neighboring waveguide induces a reactive intermode coupling in the resonator, analogous to an off-diagonal Lamb shift in atomic physics. Observable consequences of this coupling manifest as peculiar Fano line shapes in the waveguide transmission spectra. The theoretical predictions are validated by full vectorial three-dimensional finite-element numerical simulations and are confirmed by the experiments.

We present an experimental study to achieve ultrahigh optical depths for cold atomic media with a two-dimensional magneto-optical trap (MOT) of cesium. By combining large atom number, a temporally dark and compressed MOT, and Zeeman-state optical pumping, we achieve an optical depth of up to 1306 for the open transition of the cesium $D_1$ line. Our work demonstrates that it is feasible to push the optical depth up to the 1000 level with a convenient MOT setup. This development paves the way to many important proposals in quantum optics and many-body physics.

We devise and experimentally realize a procedure capable of detecting and distinguishing quantum discord and classical correlations as well the presence of factorized states in a joint system-environment setting. Our scheme builds on recent theoretical results showing how the distinguishability between two reduced states of a quantum system in a bipartite setting can convey important information about the correlations present in the bipartite state and the interaction between the subsystems. The two addressed subsystems are the polarization and spatial degrees of freedom of the signal beam generated by parametric down-conversion, which are suitably prepared by the idler beam. Different global and local operations allow for the detection of different correlations by studying via state tomography the trace distance behavior between suitable polarization subsystem states.

The standard procedure for quantum process tomography (QPT) requires a series of experiments. Each experiment involves initialization of the system to a particular basis state, applying the quantum process $\varepsilon$ on the system, and finally characterizing the output state by quantum state tomography (QST). The output states collected for a complete set of basis states enable us to calculate the $\chi$ matrix characterizing the process $\varepsilon$. The standard procedure for QST itself requires independent experiments, each involving measurement of a set of commuting observables. Thus QPT procedure demands a number of independent measurements and, moreover, this number increases rapidly with the size of the system. However, in ensemble systems, the total number of independent measurements can be greatly reduced with the availability of ancilla qubits. Ancilla-assisted process tomography (AAPT) has earlier been shown to require a single QST of system-ancilla space. Ancilla-assisted quantum state tomography (AAQST) has also been shown to perform QST in a single-scan measurement of an ensemble system. Here we combine AAPT with AAQST to realize a single-scan QPT (SSPT), a procedure to characterize a general quantum process in a single ensemble measurement. We demonstrate experimental SSPT by characterizing several single-qubit processes using a three-qubit NMR quantum register. Furthermore, using the SSPT procedure, we experimentally characterize the twirling process and compare the results with theory.

We consider a method of remote mixed state creation of a one-qubit subsystem (receiver) in a spin-1/2 chain governed by the nearest-neighbor $XY$ Hamiltonian. Owing to the evolution of the chain along with the variable local unitary transformation of the one- or two-qubit sender, a large variety of receiver states can be created during a specific time interval starting with a fixed initial state of the whole quantum system. These states form the creatable region of the receiver's state-space. It is remarkable that, with a two-qubit sender, a large creatable region may be covered at a properly fixed time instant $t_0$ using just the variable local unitary transformation of the sender. In this case we have completely local control of remote state creation. In general, for a given initial state, there are some receiver states that may not be created using the above tool. These states form the unavailable region. In turn, this unavailable region might be the creatable region of another sender. Thus, in future, we have a way to share the whole receiver's state-space among the creatable regions of several senders. The effectiveness of remote state creation is characterized by the density function of the creatable region.

We derive an inequality for three fermions with six single-particle states which reduces to the sum of the famous Coffman-Kundu-Wootters inequalities when an embedded three-qubit system is considered. We identify the quantities which are playing the role of the concurrence, the three-tangle and the invariant $det{\rho }_A+det{\rho }_B+det{\rho }_C$ for this tripartite system. We show that this latter one is almost interchangeable with the von Neumann entropy and conjecture that it measures the entanglement of one fermion with the rest of the system. We prove that the vanishing of the fermionic “concurrence” implies that the two-particle reduced-density matrix is a mixture of separable states. Also, the vanishing of this quantity is only possible in the Greenberger-Horne-Zeilinger class, where some genuine tripartite entanglement is present and in the separable class. Based on this, we conjecture that this “concurrence” measures the amount of entanglement between pairs of fermions. We identify the well-known “spin-flipped” density matrix in the fermionic context as the reduced-density matrix of a special particle-hole dual state. We show that, in general, this dual state is always canonically defined by the Hermitian inner product of the fermionic Fock space and that it can be used to calculate covariants under stochastic local operations and classical communication (SLOCC). We show that Fierz identities known from the theory of spinors relate SLOCC covariants with reduced-density-matrix elements of the state and its spin-flipped dual.

The constraint of time-integrated zero area on the laser field is a fundamental requirement, both theoretically and experimentally, in the control of molecular dynamics. By using techniques of local and optimal control theory, we show how to enforce this constraint in two benchmark control problems, namely, molecular orientation and photofragmentation. The origin and the physical implications for the dynamics of this zero-area control field are discussed.

Extensive research has been lavished on the effects of spin-orbit couplings (SOCs) in attractively interacting Fermi systems in both neutral cold-atom systems and condensed-matter systems. Recently, it was suggested that a SOC drives a class of BCS to Bose-Einstein condensate (BEC) crossover that is different from the conventional one without a SOC. Here, we explore what are the most relevant physical quantities to describe such a BCS to BEC crossover and their experimental detections. We extend the concepts of the coherence length and “Cooper-pair size” in the absence of SOC to Fermi systems with SOC. We investigate the dependence of chemical potential, coherence length, and Cooper-pair size on the SOC strength and the scattering length at three dimensions (3D) (the bound-state energy at 2D) for three attractively interacting Fermi gases with 3D Rashba, 3D Weyl, and 2D Rashba SOC, respectively. We show that only the coherence length can be used to characterize this BCS to BEC crossover. Furthermore, it is the only length which can be directly measured by radio-frequency dissociation spectra type of experiments. We stress crucial differences among the coherence length, Cooper-pair size, and the two-body bound-state size. Our results provide the fundamental and global picture of the BCS to BEC crossover and its experimental detections in various cold-atom and condensed-matter systems.

We study controllable single-photon transport in a one-dimensional waveguide with a nonlinear dispersion relation coupled to a three-level emitter in a cascade configuration. An extra cavity field is introduced to drive one of the level transitions of the emitter. In the resonance case, when the extra cavity does not contain photons, the input single photon will be reflected; when the cavity contains one photon, the full transmission of the input single photon can be obtained. In the off-resonance case, the single-photon transport can also be controlled by the parameters of the cavity. Therefore, we show that single-photon transport can be controlled by an extra cavity field.

We investigate the coupling of the spin angular momentum of light beams with elliptical polarization to the spin degree of freedom of free electrons. It is shown that this coupling, which is of similar origin as the well-known spin-orbit coupling, can lead to spin precession. The spin-precession frequency is proportional to the product of the laser field's intensity and its spin density. The electron-spin dynamics is analyzed by employing exact numerical methods as well as time-dependent perturbation theory based on the fully relativistic Dirac equation and on the nonrelativistic Pauli equation that is amended by a relativistic correction that accounts for the light's spin density.