We theoretically demonstrate the possibility of using nanomechanical systems as single-photon routers. We show how electromagnetically induced transparency in cavity optomechanical systems can be used to produce a switch for a probe field in a single-photon Fock state using very low pumping powers of a few microwatts. We present estimates of vacuum and thermal noise and show that the optimal performance of the single-photon switch is deteriorated by only a few percent even at temperatures of the order of 20 mK.

We calculated the ${}^4$He trimer and tetramer ground and excited states with the LM2M2 potential using our Gaussian expansion method for ab initio variational calculations of few-body systems. The method has been extensively used for a variety of three-, four-, and five-body systems in nuclear physics and exotic atomic and molecular physics. The trimer (tetramer) wave function is expanded in terms of symmetric three- (four-) body Gaussian basis functions, ranging from very compact to very diffuse, without assumption of any pair correlation function. The calculated results for the trimer ground and excited states are in excellent agreement with values reported in the literature. The binding energies of the tetramer ground and excited states are obtained as 558.98 and 127.33 mK (0.93 mK below the trimer ground state), respectively. We found that precisely the same shape of the short-range correlation ($r_{ij}\lesssim 4$ Å) in the dimer appears in the ground and excited states of the trimer and tetramer. The overlap function between the trimer excited state and the dimer ground state and that between the tetramer excited state and the trimer ground state are almost proportional to the dimer wave function in the asymptotic region (up to $\sim$1000 Å). Also, the pair correlation functions of trimer and tetramer excited states are almost proportional to the squared dimer wave function. We then propose a model which predicts the binding energy of the first excited state of ${}^4$He${}_N$ ($N\ge 3$) measured from the ${}^4$He${}_{N-1}$ ground state to be nearly $\frac{N}{2(N-1)}{B}_2$ where $B_2$ is the dimer binding energy.

Rydberg atoms and beams of ultracold polar molecules have become highly useful experimental tools in recent years. There is therefore a need for accessible calculations of interaction potentials between such particles and nearby surfaces and structures, bearing in mind that the particles are far out of thermal equilibrium with their environment and that their interaction is predominantly nonretarded. Based on a new perturbative expansion with respect to the inverse speed of light and the inverse conductivity, we derive a simple, closed-form expression for the interaction potential (i.e., the particle energy level shifts) of a particle and a metallic sphere that is accurate at better than the 1$\%$ level for typical experimental setups at room temperature and above and off by no more than a few percent at any temperature including zero. Our result illuminates the influence of retardation and imperfect conductivity and the interplay of these effects with geometry. The method developed for the present study may be applied to other, more complex geometries.

We study nonsequential double ionization (NSDI) processes of an atom by applying the frequency-domain theory based on the nonperturbative quantum electrodynamics. We obtain the transition formulas that describe the NSDI processes caused by the collision ionization (CI) and the collision-excitation ionization (CEI) mechanisms. By analyzing the NSDI results of each above-threshold ionization (ATI) channel, we investigate the contributions to the NSDI from the backward and forward collisions. In particular, for the CI process, the backward collision makes a major contribution to the NSDI probability, whereas for the CEI process, it depends on the characteristics of the laser-atom system: if the energy that the recolliding electron needs to excite a bound electron is much larger than the laser photon energy, such as for the case of helium in this work, the backward collision dominates the contribution; otherwise, the forward collision dominates the contribution. We also discuss the source of interference fringes in the NSDI momentum spectra due to the CI mechanism and find that the fringes can be predicted by using a simple cosine function. This work can be regarded as a development of the frequency-domain theory, which may shed light on the study of multiparticle dynamics in intense laser fields.

Usually, the oscillations of interference effects are controlled by relative phases. We show that varying the amplitudes of quantum waves, for instance by changing the reflectivity of beam splitters, can also lead to quantum oscillations and even to Bell violations of local realism. We first study theoretically a generalization of the Hong-Ou-Mandel experiment to arbitrary source numbers and beam-splitter transmittivity. We then consider a Bell-type experiment with two independent sources and find strong violations of local realism for arbitrarily large source number $N$; for small $N$, one operator measures essentially the relative phase of the sources and the other their intensities. Since, experimentally, one can measure the parity of the number of atoms in an optical lattice more easily than the number itself, we assume that the detectors measure parity.

We study the quantum statistical properties of the collective excitations of an atomic ensemble inside a high-finesse cavity. In the large-detuning regime, it is found that the virtual photon exchange can induce a long-range interaction between atoms, which results in correlated excitations. In particular, the atomic blockade phenomenon occurs when the induced long-range interaction effectively suppresses the double atomic excitation, when the average photon number takes certain values, which makes the two nearest energy levels degenerate. We also show that quantum phase transitions occur in the indirectly interacting atomic ensemble when the average photon number reaches several critical points. In this sense, the quantum statistical properties of the collective excitations are very sensitive to the change of the average photon number. Our model exhibits quantum phase transitions similar to the ones in the Lipkin-Meshkov-Glick model. Our proposal could be implemented in a variety of systems including cavity quantum electrodynamics (QED), Bose-Einstein condensates, and circuit QED.

We analyze the optical properties of one-dimensional $\mathcal{PT}$-symmetric structures of arbitrary complexity. These structures violate normal unitarity (photon flux conservation) but are shown to satisfy generalized unitarity relations, which relate the elements of the scattering matrix and lead to a conservation relation in terms of the transmittance and (left and right) reflectances. One implication of this relation is that there exist anisotropic transmission resonances in $\mathcal{PT}$-symmetric systems, frequencies at which there is unit transmission and zero reflection, but only for waves incident from a single side. The spatial profile of these transmission resonances is symmetric, and they can occur even at $\mathcal{PT}$-symmetry-breaking points. The general conservation relations can be utilized as an experimental signature of the presence of $\mathcal{PT}$ symmetry and of $\mathcal{PT}$-symmetry-breaking transitions. The uniqueness of $\mathcal{PT}$-symmetry-breaking transitions of the scattering matrix is briefly discussed by comparing to the corresponding non-Hermitian Hamiltonians.

We study the quantum correlation of photon pairs from a double Raman particle driven by laser fields in a modified photon density of states such as a cavity or a defect in a photonic crystal. We obtain an exact semianalytical expression for the photon correlation, which is characterized by two complex decay functions associated with the levels splitting (effective Rabi frequencies) that depend on the control laser field. The position and width of the cavity density of state with respect to the anti-Stokes transition determine the features in the two-photon correlation profile.

We reveal that the competition among diffraction, cubic nonlinearity, two-photon absorption, and gain localized in both space and time results in arrest of collapse, suppression of azimuthal modulation instabilities for spatiotemporal wave packets, and formation of stable three-dimensional light bullets. We show that Gaussian spatiotemporal gain landscapes support bright, fundamental light bullets, while gain landscapes featuring a ringlike spatial and a Gaussian temporal shapes may support stable vortex bullets carrying topological phase dislocations.

Bound states of asymmetric three-body systems confined to two dimensions are currently unknown. In the universal regime, two energy ratios and two mass ratios provide complete knowledge of the three-body energy measured in units of one two-body energy. We compute the three-body energy for general systems using numerical momentum-space techniques. The lowest number of stable bound states is produced when one mass is larger than two similar masses. We focus on selected asymmetric systems of interest in cold atom physics. The scaled three-body energy and the two scaled two-body energies are related through an equation for a supercircle whose radius increases almost linearly with three-body energy. The exponents exhibit an increasing behavior with three-body energy. The mass dependence is highly nontrivial. Based on our numerical findings, we give a simple relation that predicts the universal three-body energy.

We establish the optimal quantum teleportation protocol for the realistic scenario where both the input state and quantum channel are afflicted by noise. By taking these effects into account, higher fidelities are achieved. The optimality of the proposed protocol prevails even when restricted to a reduced set of generically available operations.

We study a model of dephasing (decoherence) in a two-state quantum system (qubit) coupled to a bath of harmonic oscillators. An exact analytic solution for the reduced dynamics of a two-state system in this model has been obtained previously for factorizing initial states of the combined system. We show that the model admits exact solutions for a large class of correlated initial states which are typical in the theory of quantum measurements. We derive exact expressions for the off-diagonal elements of the qubit density matrix, which hold for an arbitrary strength of coupling between the qubit and the bath. The influence of initial correlations on decoherence is considered for different bath spectral densities. Time behavior of the qubit entropy in the decoherence process is discussed.

In quantum mechanics, nonlocality (a violation of a Bell inequality) is intimately linked to complementarity, by which we mean that consistently assigning values to different observables at the same time is not possible. Nonlocality can only occur when some of the relevant observables do not commute, and this noncommutativity makes the observables complementary. Beyond quantum mechanics, the concept of complementarity can be formalized in several distinct ways. Here we describe some of these possible formalizations and ask how they relate to nonlocality. We partially answer this question by describing two toy theories which display nonlocality and obey the no-signaling principle, although each of them does not display a certain kind of complementarity. The first toy theory has the property that it maximally violates the Clauser, Horn, Shimony, and Holt (CHSH) inequality, although the corresponding local observables are pairwise jointly measurable. The second toy theory also maximally violates the CHSH inequality, although its state space is classical and all measurements are mutually nondisturbing: if a measurement sequence contains some measurement twice with any number of other measurements in between, then these two measurements give the same outcome with certainty.

We investigate the mediation of symmetry-forbidden atomic transitions using plasmonic nanostructures. We show that the excitation of the electric dipole-forbidden, quadrupole-allowed $6{}^2{S}_{1/2}-5{}^2{D}_{5/2}$ transition in cesium may be enhanced by more than 6 orders of magnitude in the intense, inhomogeneous near field of a plasmonic nanoantenna. Using optical reciprocity, the enhancement can be understood to apply to spontaneous emission as well, allowing the fast and efficient optical detection of excited atoms.

We report on an experimental investigation of rapid adiabatic passage (RAP) in a trapped barium ion system. RAP is implemented on the transition from the $6S_{1/2}$ ground state to the metastable $5D_{5/2}$ level by applying a laser at 1.76 $\mu$m. We focus on the interplay of laser frequency noise and laser power in shaping the effectiveness of RAP, which is commonly assumed to be a robust tool for high-efficiency population transfer. However, we note that reaching high state transfer fidelity requires a combination of small laser linewidth and large Rabi frequency.

A method of controlled creation of spin domains in spin-1 antiferromagnetic Bose-Einstein condensates is demonstrated. The method exploits the phenomenon of phase separation of spin components in an external potential. By using an appropriate time-dependent potential, a composition of spin domains can be created, as demonstrated in the particular cases of a double well and a periodic potential. In contrast to other methods, which rely on spatially inhomogeneous magnetic fields, here the domain structure is completely determined by the optical fields, which makes the method versatile and reconfigurable. It allows for creation of domains of various sizes, with the spatial resolution limited by the spin healing length only.

A photonic realization of the quantum field theoretical Lee model, describing the strong coupling of two neutral fermions and a neutral scalar boson field, is proposed in the ghost regime, where the Lee Hamiltonian is non-Hermitian but $\mathcal{PT}$ symmetric. Our optical system, which is based on light transport in an engineered semi-infinite waveguide lattice, could provide an accessible laboratory system to simulate $\mathcal{PT}$-symmetric quantum field theories and to visualize the appearance and role of ghost states in the dynamics.

Some exact formulas of the expectation values and probability densities in a weak measurement for an operator $\mathbf{A}$ that satisfies the property ${\mathbf{A}}^2=1$ are derived. These formulas include all-order effects of the unitary evolution due to the von Neumann interaction. These are valid not only in the weak-measurement regime, but also in the strong-measurement regime and tell us the connection between these two regimes. Using these formulas, arguments of the optimization of the signal amplification and the signal-to-noise ratio are developed in two typical experimental setups.

It is shown that theoretically viable noncontextual hidden-variable models in $d=2$ lead to conflicting dispersion-free expressions in the analysis of the conditional measurement of two non-orthogonal projectors. No satisfactory criterion of the quantum discord, which relies on the analysis of conditional measurement, is formulated in the $d=2$ hidden-variable space due to a lack of uniqueness of the dispersion-free representation. We also make a speculative comment on a “many-worlds interpretation” of hidden-variable models to account for the conditional measurement.

We study a general quantum key distribution protocol in higher dimension. In this protocol, quantum states in arbitrary $g+1$ ($1\le g\le d$) out of all $d+1$ mutually unbiased bases in a $d$-dimensional system can be used for the key encoding. This provides a natural generalization of the quantum key distribution in higher dimension and recovers the previously known results for $g=1$ and $d$. In our investigation, we study Eve's attack by two slightly different approaches. One is considering the optimal cloner of Eve, and the other, defined as the optimal attack, is maximizing Eve's information. We derive results for both approaches and show the deviation of the optimal cloner from the optimal attack. With our systematic investigation of the quantum key distribution protocols in higher dimension, one may balance the security gain and the implementation cost by changing the number of bases in the key encoding. As a side product, we also prove the equivalency between the optimal phase covariant quantum cloning machine and the optimal cloner for the $g=d-1$ quantum key distribution.