We study collective excitations of rotational and spin states of an ensemble of polar molecules, which are prepared in a dipolar crystalline phase, as a candidate for a high-fidelity quantum memory. While dipolar crystals are formed in the high-density limit of cold clouds of polar molecules under one- and two-dimensional trapping conditions, the crystalline structure protects the molecular qubits from detrimental effects of short-range collisions. We calculate the lifetime of the quantum memory by identifying the dominant decoherence mechanisms, and estimate their effects on gate operations, when a molecular ensemble qubit is transferred to a superconducting strip line cavity (circuit QED). In the case of rotational excitations coupled by dipole-dipole interactions we identify phonons as the main limitation of the lifetime of qubits. We study specific setups and conditions, where the coupling to the phonon modes is minimized. Detailed results are presented for a one-dimensional dipolar chain.

Two general variational paradigms for computing ground-state energies and properties of molecular quantum systems are (i) the parametrization of the $N$-particle wave function, as in truncated configuration interaction, which yields an upper bound on the energy in a given basis set and (ii) the constraint of the two-electron reduced-density matrix (2-RDM) by necessary $N$-representability conditions (without using the wave function) which yields a lower bound on the energy in a given basis set [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. In this paper we synthesize these two directions in a class of techniques which we call parametric variational 2-RDM methods. The 2-RDM in these methods is parametrized to be size consistent while approximately satisfying the $N$-representability conditions. We extend an energy functional of Kollmar [C. Kollmar, J. Chem. Phys. 125, 084108 (2006)], which modifies configuration interaction with double excitations to be size consistent, by including not only double but also single excitations explicitly. Using the 2-RDM parametrization, we calculate ground-state energies at both equilibrium and nonequilibrium geometries in correlation-consistent polarized valance double-zeta (cc-pVDZ) basis sets. Energies as well as properties from the parametric variational 2-RDM method, particularly at nonequilibrium geometries, are better in accuracy than those obtained from coupled cluster with single and double excitations. The present work shows clearly that, except in the dissociation of ${\text{N}}_2$, the deviation of the 2-RDM from the well-known $N$-representability conditions, such as the $D$, $Q$, and $G$ conditions, is negligible. Furthermore, calculations with helium atoms demonstrate the size consistency of the method. The computational results on $N$ representability and size consistency are especially important because they legitimatize the selected parametrization of the 2-RDM.

Calculations in the Born-Oppenheimer approximation of curves for the ground-state energy of the $\mathrm{H}_2{}^{+}$ ion vs the separation, $R$, of its protons in magnetic fields making oblique angles $\theta$ with the line connecting the protons have recently been published. It is shown here that these curves are qualitatively incorrect. The variational trial function employed fails to approximate well the wave function of the $\mathrm{H}_2{}^{+}$ ground state for oblique fields, even though this function gives very accurate results for $\theta =0$. A trial function is proposed which gives much more accurate potential curves in oblique fields. It is used to plot and tabulate ground-state binding energies for various values of $\theta$, $R$, and magnetic field strength.

The formation of the ion pair $\mathrm{H}_2{}^{+}+{\mathrm{H}}^{-}$ in electron recombination with $\mathrm{H}_3{}^{+}$ is studied. The diabatic potentials and electronic couplings are extracted from ab initio electron scattering calculations as well as quantum chemistry calculations. In order to describe this reaction we include six coupled electronic states and propagate wave packets in two dimensions using the multiconfiguration time-dependent Hartree method. Also, the cross section for ion-pair formation in electron recombination with $\mathrm{D}_3{}^{+}$ is calculated. The cross section for this isotopomer is found to be about a factor of 3 smaller than the cross section for $\mathrm{H}_3{}^{+}$.

We use a two-dimensional, two-fluid hydrodynamic model to describe the high-frequency plasmon excitations of the carbon valence electrons responding to fast ions and electric dipoles, which move parallel to a single sheet of graphene supported by an insulating substrate. We calculate the stopping and the image forces on ions and dipoles, as well as the dynamic torque on dipoles about their center of mass, resulting from the dynamic polarization of graphene. While the results for ions are similar to those obtained earlier for ion channeling through carbon nanotubes in dielectric media, the stopping and the image forces on dipoles show strong directional dependencies. The torque on point dipoles implies a strong alignment effect in the direction of motion at lower speeds, as well as a tendency of the dipole to “roll” over the graphene at high speeds.

We analyzed the two-dimensional (2D) electron momentum distributions of high-energy photoelectrons of atoms in an intense laser field using the second-order strong field approximation (SFA2). The SFA2 accounts for the rescattering of the returning electron with the target ion to first order and its validity is established by comparing with results obtained by solving the time-dependent Schrödinger equation for short pulses. By analyzing the SFA2 theory, we confirmed that the yield along the back rescattered ridge in the 2D momentum spectra can be interpreted as due to the elastic scattering in the backward directions by the returning electron wave packet. The characteristics of the extracted electron wave packets for different laser parameters are analyzed, including their dependence on the laser intensity and pulse duration. For long pulses we also studied the wave packets from the first and the later returns.

We present a systematic study of quantum phases in a one-dimensional spin-polarized Fermi gas. Three comparative theoretical methods are used to explore the phase diagram at zero temperature: the mean-field theory with either an order parameter in a single-plane-wave form or a self-consistently determined order parameter using the Bogoliubov–de Gennes equations, as well as the exact Bethe ansatz method. We find that a spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov phase, which lies between the fully paired Bardeen-Cooper-Schrieffer (BCS) state and the fully polarized normal state, dominates most of the phase diagram of a uniform gas. The phase transition from the BCS state to the Fulde-Ferrell-Larkin-Ovchinnikov phase is of second order, and therefore there are no phase separation states in one-dimensional homogeneous polarized gases. This is in sharp contrast to the three-dimensional situation, where a phase separation regime is predicted to occupy a very large space in the phase diagram. We conjecture that the prediction of the dominance of the phase separation phases in three dimension could be an artifact of the non-self-consistent mean-field approximation, which is heavily used in the study of three-dimensional polarized Fermi gases. We consider also the effect of a harmonic trapping potential on the phase diagram, and find that in this case the trap generally leads to phase separation, in accord with the experimental observations for a trapped gas in three dimensions. We finally investigate the local fermionic density of states of the Fulde-Ferrell-Larkin-Ovchinnikov ansatz. A two-energy-gap structure appears, which could be used as an experimental probe of the Fulde-Ferrell-Larkin-Ovchinnikov states.

We study the superfluid and insulating phases of bosons in double-well optical lattices, and focus on the specific example of a two-legged ladder, which is currently accessible in experiments. We obtain the zero-temperature phase diagram using both mean-field and time-evolving block decimation techniques. We find that the mean-field approach describes the correct phase boundaries only when the intrachain hopping is sufficiently small in comparison to the on-site repulsion. We show the dependence of the phase diagram on the interchain hopping or tilt between double wells. We find that the Mott-insulator phase at unit filling exhibits a nonmonotonic behavior as a function of the tilt parameter, producing a reentrant phase transition between Mott insulator and superfluid phases. Finally, we determine the critical point separating the insulating and superfluid phases at commensurate fillings, where the Berezinskii-Kosterlitz-Thouless transition occurs.

We report on the implementation of a reverse-reconciliated coherent-state continuous-variable quantum key distribution system, with which we generated secret keys at a rate of more than $2\mathrm{kb}∕\mathrm{s}$ over $25\mathrm{km}$ of optical fiber. Time multiplexing is used to transmit both the signal and phase reference in the same optical fiber. Our system includes all experimental aspects required for a field implementation of a quantum key distribution setup. Real-time reverse reconciliation is achieved by using fast and efficient low-density parity check error correcting codes.

We study experimentally superradiance in a Bose-Einstein condensate using a two-frequency pump beam. By controlling the frequency difference between the beam components, we measure the spectrum of the backward (energy-mismatched) superradiant atomic modes. In addition, we show that the populations of these modes display coherent time dynamics. These results are compared to a semiclassical model based on coupled Schrödinger-Maxwell equations.

We discuss techniques to engineer effective long-range interactions between polar molecules using external static electric and microwave fields. We consider a setup where molecules are trapped in a two-dimensional pancake geometry by a far-off-resonance optical trap, which ensures the stability of the dipolar collisions. We detail how to modify the shape and the strength of the long-range part of interaction potentials, which can be utilized to realize interesting quantum phases in the context of cold molecular gases.

We study the dynamics of the $2+1$ Dirac oscillator exactly and find spin oscillations due to a Zitterbewegung of purely relativistic origin. We find an exact mapping of this quantum-relativistic system onto a Jaynes-Cummings model, describing the interaction of a two-level atom with a quantized single-mode field. This equivalence allows us to map a series of quantum optical phenomena onto the relativistic oscillator and vice versa. We make a realistic experimental proposal, in reach with current technology, for studying the equivalence of both models using a single trapped ion.

The quantum Markovian master equation of the reduced dynamics of a harmonic oscillator coupled to a thermal reservoir is shown to possess thermal symmetry. This symmetry is revealed by a Bogoliubov transformation that can be represented by a hyperbolic rotation acting on the Liouville space of the reduced dynamics. The Liouville space is obtained as an extension of the Hilbert space through the introduction of tilde variables used in the thermofield dynamics formalism. The angle of rotation depends on the temperature of the reservoir, as well as the value of Planck’s constant. This symmetry relates the thermal states of the system at any two temperatures. This includes absolute zero, at which purely quantum effects are revealed. The Caldeira-Leggett equation and the classical Fokker-Planck equation also possess thermal symmetry. We compare the thermal symmetry obtained from the Bogoliubov transformation in related fields and discuss the effects of the symmetry on the shape of a Gaussian wave packet.

We study characteristics of superpositions and entanglement of thermal states at high temperatures and discuss their applications to quantum-information processing. We introduce thermal-state qubits and thermal-Bell states, which are a generalization of pure-state qubits and Bell states to thermal mixtures. A scheme is then presented to discriminate between the four thermal-Bell states without photon number resolving detection but with Kerr nonlinear interactions and two single-photon detectors. This enables one to perform quantum teleportation and gate operations for quantum computation with thermal-state qubits.

A formalism for quantum error correction based on operator algebras was introduced by us earlier [Phys. Rev. Lett. 98, 10052 (2007)] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical information and does not require an encoded state to be entirely in one of the corresponding subspaces or subsystems. Here, we provide detailed proofs for our earlier results, derive more results, and elucidate key points with expanded discussions. We also present several examples and indicate how the theory can be extended to operator spaces and general positive operator-valued measures.

We compute the measure of entanglement for some classes of states belonging to the simplex of Bell-diagonal states of two qutrits introduced by Baumgartner et al. [Phys. Rev. A 74, 032327 (2006)]. We discuss also partial characterization of that simplex in terms of negativity and linear entropy. A numerical exploration of the entropy-entanglement plane indicates that, in the analogy to the two-qubit case [Munro et al., Phys. Rev. A 64, 030302(R) (2001)], two-qutrit Werner states do not maximize entanglement for a given entropy.

We report the time-dependent approach to resonant electron capture into Rydberg states in collisions with molecular cations at low impact energy, as an alternative to the method based on multichannel quantum defect theory (MQDT), and present the results for the ${\mathrm{HD}}^{+}$ ion. The propagation of the initial wave function on 13 Rydberg states (besides one valence state) correctly describes the indirect dissociative recombination mechanism in the time domain. Notably, the nonlocal coupling operator between the ionization and dissociation channels is accounted for in the indirect process, extending previous work on the case of direct coupling. The present approach compares to the MQDT framework with remarkable precision: resonant structures in the cross section correctly emerge from the wave-packet propagation; the time-dependent result also forms a cross section envelope for the dense series of ultrafine MQDT resonances corresponding to the quasicontinuous part of the Rydberg state manifold.

Using a combined quantum-mechanical–classical method, we study the collisions of small Na clusters with large Ar clusters as a model for cluster deposition. We work out basic mechanisms by systematic variation of the collision energy, system sizes, and orientations. The soft Ar material is found to serve as an extremely efficient shock absorber. The collisional energy is quickly transferred at first impact, and the Na clusters are always captured by the Ar surface. The distribution of the collision energy into the Ar system proceeds very fast at the velocity of sound. The relaxation of shapes goes at a slower pace using times of several picoseconds. It produces a substantial rearrangement of the Ar system, while the Na cluster remains rather robust.

We study the dynamics of vortices in ideal and weakly interacting Bose-Einstein condensates using a Ritz minimization method to solve the two-dimensional Gross-Pitaevskii equation. For different initial vortex configurations we calculate the trajectories of the vortices. We find conditions under which a vortex-antivortex pair annihilates and is created again. For the case of three vortices we show that at certain times two additional vortices may be created, which move through the condensate and annihilate each other again. For a noninteracting condensate this process is periodic, whereas for small interactions the essential features persist, but the periodicity is lost. The results are compared to exact numerical solutions of the Gross-Pitaevskii equation confirming our analytical findings.

We investigate spontaneous emission and quantum interference effects involving a three-level atom in the vicinity of a photonic band edge beyond the weak-driving-field approximation. We consider two different three-level atoms, each subject to a probe field from the ground state and each embedded within a different photonic crystal (PhC). The first atom has the two excited states separated by a dipole transition in the optical frequency range, with this frequency being close to the surrounding PhC’s band edge. The probe field couples the ground state and the highest excited state, and is well outside the PhC band gap. If a coupling field is applied between the two upper levels, electromagnetically induced transparency (EIT) may occur, depending on the position of the band edge. The second atom has the two upper levels each dipole-coupled to the ground state and close enough that the emissions from each can coherently interfere. This atom is embedded within a PhC whose band edge lies near the lower of the two excited states, and a probe field is applied that lies just beyond this band edge. This atom exhibits a quantum interference phenomenon related to EIT called field-induced transparency, again depending on the position of the band edge relative to the lower excited state.