We consider two-color heteronuclear photoassociation of a dual-species Bose-Einstein condensate into a Bose-Einstein condensate of dipolar molecules in the $J=1$ vibronic ground state, where a free-ground laser couples atoms directly to the ground state and a free-bound laser couples the atoms to an electronically excited state. This problem raises an interest because heteronuclear photoassociation from atoms to near-ground-state molecules is limited by the small size of the target state. Nevertheless, the addition of the electronically excited state creates a second pathway for creating molecules in the vibronic ground state, leading to quantum interference between direct photoassociation and photoassociation via the excited molecular state, as well as a dispersivelike shift of the free-ground resonance position. Using LiNa as an example, these results are shown to depend on the detuning and intensity of the free-bound laser, as well as the semiclassical size of both molecular states. Whereas strong enhancement enables saturation of the free-ground transition, coherent conversion from a two-species condensate of atoms to a condensate of dipolar molecules in the vibronic ground state is only possible for a limited range of free-bound detunings near resonance.

We study the ratio between the fermion-fermion scattering length and the dimer-dimer scattering length for systems of nonrelativistic fermions, using the same functional renormalization technique as previously applied to fermionic matter. We find a strong dependence on the cutoff function used in the renormalization flow for a two-body truncation of the action. Adding a simple three-body term substantially reduces this dependence.

We investigate the condensate wave function and elementary excitations of strongly interacting bosonic polar molecules in a harmonic trap, treating the scattering amplitude beyond the standard first Born approximation (FBA). By using an appropriate trial wave function in the variational method, effects of the leading-order correction beyond the FBA have been investigated and shown to be significantly enhanced when the system is close to the phase boundary of collapse. How such a leading-order effect of going beyond the FBA can be observed in a realistic experiment is also discussed.

Strongly interacting fermionic atoms on optical lattices are studied through a Hubbard-like model Hamiltonian, in which tunneling rates of atoms and molecules between neighboring sites are assumed to be different. In the limit of large on-site repulsion $U$, the model is shown to reproduce the $t$-$J$ Hamiltonian, in which the $J$ coefficient of the Heisenberg term depends on the particle-assisted tunneling rate $g$: explicitly, $J=4g^2/U$. At half-filling, $g$ drives a crossover from a Brinkman-Rice paramagnetic insulator of fully localized atoms ($g=0$) to the antiferromagnetic Mott insulator of the standard Hubbard case ($g=t$). This is observed already in the number of doubly occupied sites under the intermediate coupling regime, thus providing a criterion for extracting from measurements the effective value of $g$.

In a near-field three-photon correlation measurement, we observed the third-order temporal and spatial correlation functions of chaotic thermal light in the single-photon counting regime. In the study, we found that the probability of jointly detecting three randomly radiated photons from a chaotic thermal source by three individual detectors is $6$ times greater if the photodetection events fall in the coherence time and coherence area of the radiation field than if they do not. From the viewpoint of quantum mechanics, the observed phenomenon is the result of three-photon interference. By making use of this property, we measured the three-photon thermal light lensless ghost image of a double spot and achieved higher visibility compared with the two-photon thermal light ghost image.

We propose and analyze a multifunctional setup consisting of high-finesse optical cavities, beam splitters, and phase shifters. The basic scheme projects arbitrary photonic two-mode input states onto the subspace spanned by the product of Fock states $|n\rangle |n\rangle$ with $n=0,1,2,\dots .$ This protocol does not only provide the possibility to conditionally generate highly entangled photon number states as resource for quantum information protocols but also allows one to test and hence purify this type of quantum states in a communication scenario, which is of great practical importance. The scheme is especially attractive as a generalization to many modes allows for distribution and purification of entanglement in networks. In an alternative working mode, the setup allows for quantum nondemolition number resolved photodetection in the optical domain.

We predict that stable mobile spatiotemporal solitons can exist in arrays of periodically curved optical waveguides. We find two-dimensional light bullets in planar arrays with harmonic waveguide bending and three-dimensional bullets in square lattices with helical waveguide bending using variational formalism. Stability of the light-bullet solutions is confirmed by the direct numerical simulations which show that the light bullets can freely move across the curved arrays. This mobility property is a distinguishing characteristic compared to previously considered discrete light bullets which were trapped to a specific lattice site. These results suggest new possibilities for flexible spatiotemporal manipulation of optical pulses in photonic lattices.

For a particle of mass $m$ that obeys the time-independent Dirac equation in one dimension with a symmetric potential, Unanyan et al. [Phys. Rev. A 79, 044101 (2009)] recently pointed out that the inequality $\Delta x=\sqrt{\langle x^2}\rangle >\lambda /2$ can be derived simply from the Dirac equation. Here $\lambda =\hslash /(\mathit{mc})$ is the Compton wavelength, $x$ is the particle coordinate, and $\langle x^2\rangle$ is the expectation value of $x^2$. We conjecture that a new, more stringent limit $\Delta x⩾\lambda /\sqrt{2}$ holds for any symmetric potential. We present a model analysis on which the conjecture is based.

We study in detail the coherent interference mechanism leading to the intermediate-field two-photon absorption enhancement recently found for shaped femtosecond pulses with spectral phases that are antisymmetric around one-half of the transition frequency. We particularly investigate the tolerance of the phenomenon to the phase deviation from perfect antisymmetry. We theoretically and experimentally find that this tolerance increases as the field strength increases. For the present Na excitation, the enhancement occurs even when $~$30% of the phase pattern is not antisymmetric. Our findings are of particular importance for multichannel coherent control scenarios.

We consider the dynamical behavior of a nanomechanical mirror in a high-quality cavity under the action of a coupling laser and a probe laser. We demonstrate the existence of the analog of electromagnetically induced transparency (EIT) in the output field at the probe frequency. Our calculations show explicitly the origin of EIT-like dips as well as the characteristic changes in dispersion from anomalous to normal in the range where EIT dips occur. Remarkably the pump-probe response for the optomechanical system shares all the features of the $\Lambda$ system as discovered by Harris and collaborators.

The ability to unconditionally verify the location of a communication receiver would lead to a wide range of new security paradigms. However, it is known that unconditional location verification in classical communication systems is impossible. In this work we show how unconditional location verification can be achieved with the use of quantum communication channels. Our verification remains unconditional irrespective of the number of receivers, computational capacity, or any other physical resource held by an adversary. Quantum location verification represents an application of quantum entanglement that delivers a feat not possible in the classical-only channel. It gives us the ability to deliver real-time communications viable only at specified geographical coordinates.

As a practical method, the passive scheme is useful to monitor the photon statistics of an untrusted source in a “Plug & Play” quantum key distribution (QKD) system. In a passive scheme, three kinds of monitor mode can be adopted: average photon number (APN) monitor, photon number analyzer (PNA), and photon number distribution (PND) monitor. In this paper, the security analysis is rigorously given for the APN monitor, while for the PNA, the analysis, including statistical fluctuation and random noise, is addressed with a confidence level. The results show that the PNA can achieve better performance than the APN monitor and can asymptotically approach the theoretical limit of the PND monitor. Also, the passive scheme with the PNA works efficiently when the signal-to-noise ratio (${\mathrm{R}}^{\mathrm{SN}}$) is not too low and so is highly applicable to solve the untrusted source problem in the QKD system.

We model combined photoassociation and Feshbach resonances in a Bose-Einstein condensate, where the shared dissociation continuum allows for quantum interference in losses from the condensate, as well as a dispersive-like shift of resonance. A seemingly oversimplified model is revisited, explaining it as based on the limit of weakly bound molecules, reinforcing it with a comparison to numerical experiments that explicitly include dissociation to noncondensate modes, comparing it against the unitarity limit on condensate losses, and lastly, checking its universal implications. In particular, for a resonant laser and an off-resonant magnetic field, these numerical experiments reveal a rate limit on condensate losses that is larger for smaller condensate densities, approaches the rate limit for magnetoassociation alone near the Feshbach resonance, and agrees best with the analytical model for low density. Comparing the analytical rate limit against the unitary limit, which is set by the size of the condensate, agreement is found only for a limited range of near-resonant magnetic fields. Finally, for a resonant magnetic field and an off-resonant laser, the analytical shift of the Feshbach resonance is found to depend on the size of the Feshbach molecule, signifying nonuniversal physics in a strongly interacting system.

We propose an all-optical scheme to probe the dynamical correlations of a strongly interacting gas of ultracold atoms in an optical lattice potential. The proposed technique is based on a pump-and-probe scheme: a coherent light pulse is initially converted into an atomic coherence and later retrieved after a variable storage time. The efficiency of the proposed method to measure the two-time one-particle Green function of the gas is validated by numerical and analytical calculations of the expected signal for the two cases of a normal Fermi gas and a BCS superfluid state. Protocols to extract the superfluid gap and the full quasiparticle dispersions are discussed.

At long distances, interactions between neutral ground-state atoms can be described by the van der Waals potential. In the ultracold regime, atom-atom scattering is dominated by $s$-waves phase shifts given by an effective range expansion in terms of the scattering length ${\alpha }_0$ and the effective range $r_0$. We show that while the scattering length cannot be predicted for these potentials, the effective range is given by the universal low-energy theorem $r_0=A+B/{\alpha }_0+C/{\alpha }_0^2$, where $A$, $B$, and $C$ depend on the dispersion coefficients $C_n$ and the reduced diatom mass. We confront this formula to about 100 determinations of $r_0$ and ${\alpha }_0$ and show why the result is dominated by the leading dispersion coefficient $C_6$. Universality and scaling extend much beyond naive dimensional analysis estimates.

We apply quantum control techniques to a long spin chain by acting only on two qubits at one of its ends, thereby implementing universal quantum computation by a combination of quantum gates on these qubits and indirect swap operations across the chain. It is shown that the control sequences can be computed and implemented efficiently. We discuss the application of these ideas to physical systems such as superconducting qubits in which full control of long chains is challenging.

The random-dimer model is probably the most popular model for a one-dimensional disordered system where correlations are responsible for delocalization of the wave functions. This is the primary model used to justify the insulator-metal transition in conducting polymers and in DNA. However, for such systems, the localization-delocalization regimes have only been observed by deeply modifying the system itself, including the correlation function of the disordered potential. In this article, we propose to use an ultracold atomic mixture to cross the transition simply by externally tuning the interspecies interactions and without modifying the impurity correlations.

A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated. An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron’ko-Stroganov model.

Given an experimental setup and a fixed number of measurements, how should one take data to optimally reconstruct the state of a quantum system? The problem of optimal experiment design (OED) for quantum state tomography was first broached by Kosut et al. [R. Kosut, I. Walmsley, and H. Rabitz, e-print arXiv:quant-ph/0411093 (2004)]. Here we provide efficient numerical algorithms for finding the optimal design, and analytic results for the case of ‘minimal tomography’. We also introduce the average OED, which is independent of the state to be reconstructed, and the optimal design for tomography (ODT), which minimizes tomographic bias. Monte Carlo simulations confirm the utility of our results for qubits. Finally, we adapt our approach to deal with constrained techniques such as maximum-likelihood estimation. We find that these are less amenable to optimization than cruder reconstruction methods, such as linear inversion.