We propose a scheme that utilizes the collective enhancement of a photonic mode inside an atomic ensemble together with a proper Zeeman manifold to achieve a heralded polarization entangled Bell state. The entanglement is between two photons that are separated in time and can be used as a postselected deterministic source for applications such as quantum repeaters where a subsequent entanglement swapping measurement is employed. We present a detailed analysis of the practical limitation of the scheme.

We report the direct observation of the orientation of jet-cooled molecules induced by a THz pulse. The intense THz field ($\sim$30 kV/cm) creates a superposition between the rotational ground state ($J=0$) and the excited state ($J=1$) of HBr molecules. The rotational dynamics is probed by Coulomb explosion imaging of the fragment ions produced by a near-infrared femtosecond laser pulse. Comparing with the simulations based on a time-dependent Schrödinger equation, the rotational wave packets are completely reconstructed, which reveal that $\sim$$7\times {10}^{-4}$ of the ground-state population is transferred to the $J=1$ state at an initial temperature of 8 K, achieving a degree of orientation of $\langle cos\theta \rangle \sim 0.017$.

We use direct spatial ion imaging of cold ${}^{85}$Rb Rydberg atom clouds to measure the Rydberg-Rydberg correlation function, with and without light-shift potentials generated by an optical dipole trap. We find that the blockade radius depends on laser detunings and spatially varying light shifts. At certain laser detunings the probability of exciting Rydberg atoms at particular separations is enhanced, which we interpret to be a result of direct two-photon excitation of Rydberg atom pairs. The results are in accordance with predictions [F. Robicheaux and J. V. Hernández, Phys. Rev. A 72, 063403 (2005)] and a model we develop that accounts for a one-dimensional dipole-trap potential.

We propose a linear compression technique for the time-interval distribution of photon pairs. Using a partially frequency-entangled two-photon (TP) state with an appropriate mean time width, the compressed TP time-interval width can be kept in the minimum limit set by the phase modulation, and is independent of its initial width. In addition, the ultranarrow TP time-interval distribution can be compressed with relatively slow phase modulators to decrease damage from the phase instability that arises from the phase modulation process.

Monogamy inequalities for the way bipartite Einstein-Podolsky-Rosen (EPR) steering can be distributed among $N$ systems are derived. One set of inequalities is based on witnesses with two measurement settings, and may be used to demonstrate correlation of outcomes between two parties, that cannot be shared with more parties. It is shown that the monogamy for steering is directional. Two parties cannot independently demonstrate steering of a third system, using the same two-setting steering witness, but it is possible for one party to steer two independent systems. This result explains the monogamy of two-setting Bell inequality violations and the sensitivity of the continuous variable (CV) EPR criterion to losses on the steering party. We generalize to $m$ settings. A second type of monogamy relation gives the quantitative amount of sharing possible, when the number of parties is less than or equal to $m$, and takes a form similar to the Coffman-Kundu-Wootters relation for entanglement. The results enable characterization of the tripartite steering for CV Gaussian systems and qubit Greenberger-Horne-Zeilinger and $W$ states.

We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control methods to significantly reduce the number of signal coefficients that are required for reconstruction of time-varying parameters with high fidelity. We show that incoherent measurement bases and, more generally, suitable random measurement matrices can be created by performing simple control sequences on the quantum system. Random measurement matrices satisfying the restricted isometry property can be used efficiently to reconstruct signals that are sparse in any basis. Because many physical processes are approximately sparse in some basis, these methods can benefit a variety of applications such as quantum sensing and magnetometry with nitrogen-vacancy centers.

We study the dynamics of the entanglement structure of a multipartite system experiencing a dissipative evolution. We characterize the processes leading to a particular form of output-system entanglement and provide a recipe for their identification via concatenations of particular linear maps with entanglement-breaking operations. We illustrate the applicability of our approach by considering local and global depolarizing noises acting on general multiqubit states. A difference in the typical entanglement behavior of systems subjected to these noises is observed: the originally genuine entanglement dissociates by splitting off particles one by one in the case of local noise, whereas intermediate stages of entanglement clustering are present in the case of global noise. We also analyze the definitive phase of evolution when the annihilation of the entanglement compound finally takes place.

The majority of quantum-error-detection and correction protocols assume that the population in a qubit does not leak outside of its computational subspace. For many existing approaches, however, the physical qubits do possess more than two energy levels and consequently are prone to such leakage events. Analyzing the effects of leakage is therefore essential to devise optimal protocols for quantum gates, measurement, and error correction. In this article, we present a detailed study of leakage in a two-qubit superconducting stabilizer measurement circuit. We simulate the repeated ancilla-assisted measurement of a single ${\sigma }^z$ operator for a data qubit, record the outcome at the end of each measurement cycle, and explore the signature of leakage events in the obtained readout statistics. An analytic model is also developed that closely approximates the results of our numerical simulations. We find that leakage leads to destructive features in the quantum-error-detection scheme, making additional hardware and software protocols necessary.

The separability from spectrum problem asks for a characterization of the eigenvalues of the bipartite mixed states $\rho$ with the property that $U^{†}\rho U$ is separable for all unitary matrices $U$. This problem has been solved when the local dimensions $m$ and $n$ satisfy $m=2$ and $n\le 3$. We solve all remaining qubit-qudit cases (i.e., when $m=2$ and $n\ge 4$ is arbitrary). In all of these cases we show that a state is separable from spectrum if and only if $U^{†}\rho U$ has positive partial transpose for all unitary matrices $U$. This equivalence is in stark contrast with the usual separability problem, where a state having positive partial transpose is a strictly weaker property than it being separable.

We address and quantify the role of nonadiabaticity (“memory effects”) in the exchange-correlation (xc) functional of time-dependent density functional theory (TDDFT) for describing nonlinear dynamics of many-body systems. Time-dependent resonant processes are particularly challenging for available TDDFT approximations, due to their strong nonlinear and nonadiabatic character. None of the known approximate density functionals are able to cope with this class of problems in a satisfactory manner. In this work we look at the prototypical example of the resonant processes by considering Rabi oscillations within the exactly soluble two-site Hubbard model. We construct the exact adiabatic xc functional and show that (i) it does not reproduce correctly resonant Rabi dynamics, and (ii) there is a sizable nonadiabatic contribution to the exact xc potential, which turns out to be small only at the beginning and at the end of the Rabi cycle when the ground-state population is dominant. We then propose a “two-level” approximation for the time-dependent xc potential which can capture Rabi dynamics in the two-site problem. It works well both for resonant and for detuned Rabi oscillations and becomes essentially exact in the linear response regime.

Perfluorocarbons (PFCs) are man-made compounds whose ion physics exhibit complex interplays between statistical and nonstatistical fragmentation and intramolecular rearrangement processes. One probe of such processes is the energy-dependent electron-impact-ionization cross section. Partial electron-impact-ionization cross sections are reported for the fragments arising from five C${}_2$ to C${}_4$ PFCs, namely, C${}_2$F${}_6$, C${}_3$F${}_8$, C${}_3$F${}_6$, CF${}_2$=CF-CF=CF${}_2$, and CF${}_3$-C≡C-CF${}_3$, over the energy range from threshold to ∼210 eV. Care was taken to maximize ion collection efficiency and to minimize discrimination against ions produced with high kinetic-energy release, and the measured cross sections have been calibrated using independent absolute total (gross) ionization efficiency curves measured previously in the same laboratory with an instrument that was designed to essentially have unit detection efficiency. Total ionization cross sections have also been modeled using the binary-encounter Bethe model, and the shortcomings of the model when applied to perfluorinated compounds are discussed. Analysis of the mass spectral fragmentation patterns in combination with ab initio energetics suggests that nonstatistical dissociative ionization processes play a significant role in the fragmentation dynamics of saturated PFCs. In contrast, unsaturated PFCs exhibit long-lived parent ions, which tend to undergo a higher degree of statistical dissociation following ionization, involving considerable intramolecular rearrangement.

We propose an operating condition for an optically pumped scalar atomic magnetometer with a unique band-pass frequency response. Under this operating condition, the signal response of the magnetometer is increased threefold around a nonzero resonance frequency. The resonance frequency is equal to the detuning between the Larmor frequency and the frequency of the oscillating magnetic field used for excitation. The resonance is explained in terms of the characteristics of the first-order perturbation expansion of the Bloch equation for a modulated bias magnetic field. The scalar magnetometer provides an enhanced magnetic response around its resonance frequency even beyond the cutoff frequency, which is defined as the inverse of the phase relaxation time of the spin polarization.

We investigate the entanglement between electronic and vibrational degrees of freedom produced by a vibronic coupling in a molecular system described in the Born-Oppenheimer approximation. Entanglement in a pure state of the Hilbert space $\mathcal{H}={\mathcal{H}}_{\mathrm{el}}⨂{\mathcal{H}}_{\mathrm{vib}}$ is quantified using the von Neumann entropy of the reduced density matrix and the reduced linear entropy. Expressions for these entanglement measures are derived for the $2\times N_v$ and $3\times N_v$ cases of the bipartite entanglement, where 2 and 3 are the dimensions of the electronic Hilbert space $\mathcal{H}$${}_{\mathrm{el}}$, and $N_v$ is the dimension of $\mathcal{H}$${}_{\mathrm{vib}}$. We study the entanglement dynamics for two electronic states coupled by a laser pulse (a $2\times N_v$ case), taking as an example a coupling between the $a^3{{\Sigma }_u}^{+}(6s,6s)$ and $1_g(6s,6p_{3/2})$ states of the Cs${}_2$ molecule. The reduced linear entropy expression obtained for the $3\times N_v$ case is used to follow the entanglement evolution in a scheme proposed for the control of the vibronic dynamics in a Cs${}_2$ cold molecule, implying the $a^3{{\Sigma }_u}^{+}(6s,6s)$, $0_g{}^{-}(6s,6p_{3/2})$, and $0_g{}^{-}(6s,5d)$ electronic states, which are coupled by a nonadiabatic radial coupling and a sequence of chirped laser pulses.

We perform a Bohmian-trajectory analysis of high-order-harmonic generation (HHG), focusing on the fact that typical HHG spectra are best reproduced by the Bohmian trajectory starting at the innermost part of the core [J. Wu, B. B. Augstein, and C. Figueira de Morisson Faria, Phys. Rev. A 88, 023415 (2013)]. Using ensemble averages around this central trajectory, we show that for the high-plateau and cutoff harmonics, small ensembles of Bohmian trajectories are sufficient for a quantitative agreement with the numerical solution of the time-dependent Schrödinger equation (TDSE), while larger ensembles are necessary in the low-plateau region. Furthermore, we relate the Bohmian trajectories to the short and long trajectories encountered in the strong-field approximation (SFA) and show that the time-frequency maps from the central Bohmian trajectory overestimate the contributions of the long SFA trajectory, in comparison to the outcome of the TDSE computations. We also discuss how the time-frequency profile of the central trajectory may be influenced nonlocally by degrading the wave-packet propagation far from the core.

We experimentally investigate lasing behaviors of population-inverted N${}_2$ ions for the transitions between the vibrational level ($v$′ = 0) of excited electronic $B$ Σ${}_u$${}^{+}$ state and the two lowest vibrational levels ($v$ = 0, 1) of the ground $X$ Σ${}_g$${}^{+}$ state in an elliptically polarized laser field. It is found that, as the polarization of the pump laser evolves from linear to circular, the lasing signal for the 0 → 0 transition at 391 nm first increases with a maximum enhancement of ∼40% at the ellipticity of 0.3 and then decreases, whereas for the 0 → 1 transition at 428 nm, the lasing signal decreases monotonically. This difference between the 391- and 428-nm lasing signals is ascribed to the high sensitivity of the strong-field response of the molecular ion to molecular vibrations, which indicates the possibility to control the vibrational state distribution of molecules by tuning the ellipticity of the laser pulse.

We study two-dimensional (2D) solitons in the mean-field models of ultracold gases with long-range quadrupole-quadrupole interaction (QQI) between particles. The condensate is loaded into a deep optical-lattice (OL) potential, therefore the model is based on the 2D discrete nonlinear Schrödinger equation with contact on site and long-range intersite interactions, which represent the QQI. The quadrupoles are built as pairs of electric dipoles and antidipoles orientated perpendicular to the 2D plane to which the gas is confined. Because the quadrupoles interact with the local gradient of the external field, they are polarized by an inhomogeneous dc electric field that may be supplied by a tapered capacitor. Shapes, stability, mobility, and collisions of fundamental discrete solitons are studied by means of systematic simulations. In particular, threshold values of the norm, which are necessary for the existence of the solitons, are found and anisotropy of their static and dynamical properties is explored. As concerns the mobility and collisions, we analyze such properties for discrete solitons on 2D lattices with long-range intersite interactions. Estimates demonstrate that the setting can be realized under experimentally available conditions, predicting solitons built of $\sim 10000$ particles.

We investigate the breathing mode of harmonically trapped bosons in an optical lattice at small site occupancies. The Bose-Hubbard model with a trapping potential is used to describe the breathing-mode dynamics initiated through weak quenches of the trap strength. We connect to results for continuum bosons (Lieb-Liniger and Gross-Pitaevskii results) and also present deviations from continuum physics. We take a spectral perspective, identifying the breathing-mode frequency with a particular energy gap in the spectrum of the trapped Bose-Hubbard Hamiltonian. We present the low-energy eigenspectrum of the trapped many-boson system and study overlaps of the initial state with eigenstates of the quenched Hamiltonian. There is an intermediate interaction regime, between a “free-boson” limit and a “free-fermion” limit, in which the Bose-Hubbard breathing-mode frequency approaches the Gross-Pitaevskii prediction. In addition, we present a striking failure of the time-dependent Gutzwiller approximation for describing breathing modes.

We investigate the superfluidity of attractive Fermi gas in a square optical lattice with spin-orbit coupling (SOC). We show that the system displays a variety of new features. At half filling, SOC induces a Dirac semimetal and the system undergoes a semimetal-superfluid transition. Near half filling, we find that the superfluidity tends to be suppressed due to the emerging Dirac cones. While for small fillings, SOC can induce a BCS-BEC crossover beyond the conventional attractive Hubbard model, which is characterized by a bound state in the lattices. Moreover, we demonstrate that the superfluid density also exhibits many unusual properties in the lattices.

We present a theory for the Landau damping of low-energy quasiparticles in a collisionless, quasi-two-dimensional dipolar Bose gas and produce expressions for the damping rate in uniform and nonuniform systems. Using simple energy-momentum conservation arguments, we show that in the homogeneous system, the nature of the low-energy dispersion in a dipolar Bose gas severely inhibits Landau damping of long wavelength excitations. For a gas with contact and dipolar interactions, the damping rate for phonons tends to decrease with increasing dipolar interactions; for strong dipole-dipole interactions, phonons are virtually undamped over a broad range of temperature. The damping rate for maxon-roton excitations is found to be significantly larger than the damping rate for phonons.