A simple method of analyzing quantum feedback circuits is presented. The classical analysis of feedback circuits can be generalized to apply to quantum systems by mapping the field operators of various outputs to other inputs via the standard input-output formalism. Unfortunately, this has led to unphysical results such as the violation of the Heisenberg uncertainty principle for in-loop fields. This paper shows that this general approach can be redeemed by ensuring a self-consistently Hermitian Hamiltonian. The calculations are based on a noncommutative calculus of operator derivatives. A full description of several examples of quantum linear and nonlinear feedback for optical systems is presented.

We study the probabilistic cloning of three symmetric states. These states are defined by a single complex quantity, the inner product among them. We show that three different probabilistic cloning machines are necessary to optimally clone all possible families of three symmetric states. We also show that the optimal cloning probability of generating $M$ copies out of one original can be cast as the quotient between the success probability of unambiguously discriminating one and $M$ copies of symmetric states.

For a finite-dimensional bipartite system, the relation between local projections and post-selected state dependence on the global state submatrices is given in a general setting. As a result joint state reconstruction is derived with strict local projective measurements and one-way classical communication, reducing the number of detectors in comparison to standard procedures. Generalization to multipartite systems is given, also reducing the number of detectors for multiqubits.

Since, in general, nonorthogonal states cannot be cloned, any eavesdropping attempt in a quantum-communication scheme using nonorthogonal states as carriers of information introduces some errors in the transmission, leading to the possibility of detecting the spy. Usually, orthogonal states are not used in quantum-cryptography schemes since they can be faithfully cloned without altering the transmitted data. Nevertheless, L. Goldberg and L. Vaidman [Phys. Rev. Lett. 75, 1239 (1995)] proposed a protocol in which, even if the data exchange is realized using two orthogonal states, any attempt to eavesdrop is detectable by the legal users. In this scheme the orthogonal states are superpositions of two localized wave packets traveling along separate channels. Here we present an experiment realizing this scheme.

We study the time-dependent density-functional theory formulation of nonadiabatic couplings (NAC’s) to settle problems regarding practical calculations. NAC’s have so far been rigorously formulated on the basis of the density response scheme and expressed using the nuclear derivative of the Hamiltonian, $\partial H/\partial R$, whereby causing the pseudopotential problem. When rewritten using the nuclear derivative operator, $\partial /\partial R$, or the $d$ operator, the formula is found free of the problem and thus provides a working numerical scheme. The $d$-operator-based formulation also allows us to lay a foundation on the empirical Slater transition-state method and to show an improved way of using the auxiliary excited-state wave-function ansatz, both of which have been utilized in previous works. Evaluation of NAC near either the Jahn-Teller or the Renner-Teller intersection in various molecular systems shows that the values of NAC are much improved over previous calculations when the $d$-operator formula is implemented in the pseudopotential framework.

Nonrelativistic, relativistic, quantum electrodynamic, and finite nuclear mass corrections to the energy levels are obtained for the ${\mathit{nS}}_{1/2},n=3,\dots ,9$ states of the lithium atom. Computational approach is based on the explicitly correlated Hylleraas functions with the analytic integration and recursion relations. Theoretical predictions for the ionization potential of ${\mathit{nS}}_{1/2}$ states and transition energies ${\mathit{nS}}_{1/2}\to 2S_{1/2}$ are compared to known experimental values for ${}^{6,7}\mathrm{Li}$ isotopes.

In the present paper, we show that the absorption of a single photon can singly ionize both atoms of a helium dimer (He${}_2$): ionization with simultaneous excitation of one atom followed by de-excitation via interatomic Coulombic decay leads to the ejection of an electron from each of the the two atoms of the dimer. Using the Cold Target Recoil Ion Momentum Spectroscopy technique (COLTRIMS), we obtained angular distributions of these electrons in the laboratory frame and the molecular frame. We observe a pronounced variation of these distributions for different regions of kinetic-energy releases of the ions.

Experimental measurements of photoionization rates of ${\mathit{nD}}_{5/2}$ Rydberg states of Cs ($50⩽n⩽75$) in a 1064-nm far off-resonance dipole trap are presented. The photoionization rates are obtained by measuring the lifetimes of Rydberg atoms produced inside of a 1064-nm far off-resonance trap and comparing the lifetimes to corresponding control experiments in a magneto-optical trap. Experimental results for the control experiments agree with recent theoretical predictions for Rydberg state lifetimes and measured photoionization rates are in agreement with transition rates calculated from a model potential.

We show how the momentum distribution of gaseous Bose-Einstein condensates can be shaped by applying a sequence of standing-wave laser pulses. We present a theory, whose validity was demonstrated in an earlier experiment [L. Deng et al., Phys. Rev. Lett. 83, 5407 (1999)], of the effect of a two-pulse sequence on the condensate wavefunction in momentum space. We generalize the previous result to the case of $N$ pulses of arbitrary intensity separated by arbitrary intervals and show how these parameters can be engineered to produce a desired final momentum distribution. We find that several momentum distributions, important in atom-interferometry applications, can be engineered with high fidelity with two or three pulses.

We generalize the application of small polaron theory to ultracold gases [M. Bruderer, A. Klein, S. R. Clark, and D. Jaksch, New J. Phys. 10, 033015 (2008)] to the case of Bose-Fermi mixtures, where both components are loaded into an optical lattice. In a suitable range of parameters, the mixture can be described within a Bogoliubov approach in the presence of fermionic (dynamic) impurities; an effective description in terms of polarons applies. In the dilute limit of the slow-impurity regime, the hopping of fermionic particles is exponentially renormalized due to polaron formation, regardless of the sign of the Bose-Fermi interaction. This should lead to clear experimental signatures of polaronic effects, once the regime of interest is reached. The validity of our approach is analyzed in the light of currently available experiments. We provide results for the hopping renormalization factor for different values of temperature, density, and Bose-Fermi interaction for three-dimensional ${}^{87}\mathrm{Rb}$-${}^{40}\mathrm{K}$ mixtures in an optical lattice.

We introduce two models of quasidiscrete optical systems: an array of waveguides doped by four-level $N$-type atoms, and a nonlinear checkerboard pattern, formed by doping with three-level atoms of the $\Lambda$-type. The dopant atoms are driven by external fields, to induce the effect of the electromagnetically induced transparency (EIT). These active systems offer advantages and additional degrees of freedom, in comparison with ordinary passive waveguiding systems. In the array of active waveguides, the driving field may adjust linear and nonlinear propagation regimes for a probe signal. The nonlinear checkerboard system supports the transmission of stable spatial solitons and their “fuzzy” counterparts, straight or oblique.

Ghost imaging for the reflected object with rough surface is investigated. The surface height variance ${\sigma }_h^2$ and the correlation length $l_c$ have been introduced to characterize the rough surface. Based on a simple scattering model, we derive the analytical expressions which are used to describe the effects of ${\sigma }_h^2$ and $l_c$ on ghost imaging. The results show that both ${\sigma }_h^2$ and $l_c$ have no influence on the image resolution, while the convergence of the correlation decreases as ${\sigma }_h^2$ increases. Additionally, the bucket detector used in the test arm can dramatically improve the visibility of ghost images. The results are backed up by numerical simulations, in which a Monte Carlo approach to generate a rough surface has been used.

Strong nonlinearity plays a significant role in physics, particularly in the design of novel quantum sources of light and matter as well as in quantum chemistry and quantum biology. In simple systems, the photon-photon interaction can be determined analytically. However, it becomes challenging to obtain it for more complex systems. Therefore, we show here how to measure strong nonlinearities by allowing the sample to interact with a weakly pumped quantized leaking optical mode. We found that the detected mean photon number versus pump-field frequency shows several peaks. Interestingly, the interval between neighboring peaks equals the photon-photon interaction potential. Furthermore, the system exhibits sub-Poissonian photon statistics, entanglement, and photon switching with less than one photon. Finally, we connect our study with existing experiments.

We provide a simple class of 2-qudit states for which one is able to formulate necessary and sufficient conditions for separability. As a by-product, we generalize the well-known construction provided by Horodecki et al. [Phys. Rev. Lett. 82, 1056 (1999)] for $d=3$. It is hoped that these states with known separability and entanglement properties may be used to test various notions in entanglement theory.

We consider a macroscopic two-state system based on persistent current states of a Bose-Einstein condensate (BEC) of interacting neutral atoms confined in a ring with a weak Josephson link. We demonstrate that macroscopic superpositions of different BEC flows are energetically favorable in this system. Moreover, a macroscopic two-state dynamics emerges in the low-energy limit. We also investigate fundamental limitations due to the noise inherent in the interacting BEC of Josephson-ring geometry. We show that the coherent macroscopic dynamics is readily measurable for an experimentally accessible range of parameters.

Two-component Fermi and Bose gases with infinitely large interspecies $s$-wave scattering length $a_s$ exhibit a variety of intriguing properties. Among these are the scale invariance of two-component Fermi gases with equal masses, and the favorable scaling of Efimov features for two-component Bose gases and Bose-Fermi mixtures with unequal masses. This paper builds on our earlier work [Phys. Rev. Lett. 105, 170403 (2010)] and presents a detailed discussion of our studies of small unequal-mass two-component systems with infinite $a_s$ in the regime where three-body Efimov physics is absent. We report on nonuniversal few-body resonances. Just like with two-body systems on resonance, few-body systems have a zero-energy bound state in free space and a diverging generalized scattering length. Our calculations are performed within a nonperturbative microscopic framework and investigate the energetics and structural properties of small unequal-mass two-component systems as functions of the mass ratio $\kappa$, and the numbers $N_1$ and $N_2$ of heavy and light atoms. For purely attractive Gaussian two-body interactions, we find that the $(N_1,N_2)=(2,1)$ and $(3,1)$ systems exhibit three-body and four-body resonances at mass ratios $\kappa =12.314(2)$ and $10.4(2)$, respectively. The three- and four-particle systems on resonance are found to be large. It seems feasible that the features discussed in this paper can be probed experimentally with present-day technology.

We investigate the quantum electrodynamic (QED) properties of an atomic electron close to the focus of a spherical mirror. We first show that the spontaneous emission and excited-state level shift of the atom can be fully suppressed with mirror-atom distances of many wavelengths. A three-dimensional theory predicts that the spectral density of vacuum fluctuations can indeed vanish within a volume ${\lambda }^3$ around the atom, with the use of a far-distant mirror covering only half of the atomic emission solid angle. The modification of these QED atomic properties is also computed as a function of the mirror size, and large effects are found for only moderate numerical apertures. We also evaluate the long-distance ground-state energy shift (Casimir-Polder shift) and find that it scales as $(\lambda /R){}^2$ at the focus of a hemispherical mirror of radius $R$, as opposed to the well-known $(\lambda /R){}^4$ scaling law for an atom at a distance $R$ from an infinite plane mirror. Our results are relevant for investigations of QED effects as well as free-space coupling to single atoms using high-numerical-aperture lenses.

We report ab initio relativistic correlation calculations of potential curves and spectroscopic constants for the four lowest-lying electronic states of lead monofluoride. We also calculated parameters of the spin-rotational Hamiltonian for the ground ${}^2{\Pi }_{1/2}$ and the first excited $A$ ${}^2{\Sigma }_{1/2}^{+}$ states including P,T-odd and $P$-odd terms. In particular, we have obtained hyperfine constants of the ${}^{207}\mathrm{Pb}$ nucleus. For the ${}^2{\Pi }_{1/2}$ state, $A_{\perp }=-6859.6$ MHz, $A_{\Vert }=9726.9$ MHz and for the $A$ ${}^2{\Sigma }_{1/2}^{+}$ state, $A_{\perp }=1720.8$ MHz, $A_{\Vert }=3073.3$ MHz. Our values of the ground-state hyperfine constants are in good agreement with previous theoretical studies. We discuss and explain seeming disagreement with the recent experimental data of the sign of the constant $A_{\perp }$. The effective electric field on the electron $E_{\mathrm{eff}}$, which is important in the planned experiment for searching for the electric dipole moment of the electron, is found to be $3.3\times {10}^{10}\hspace{0.5em}\mathrm{V}/\mathrm{cm}$.

The carrier-envelope phase (CEP) of high-peak-power, many-cycle laser fields becomes a crucial parameter when such fields are used, in conjunction with polarization gating techniques, in isolated attosecond (asec) pulse generation. However, its measurement has not been achieved so far. We demonstrate a physical process sensitive to the CEP value of such fields and describe a method for its online shot-to-shot monitoring. This work paves the way for the exploitation of energetic isolated asec pulses in studies of nonlinear extreme ultraviolet (XUV) processes and XUV-pump–XUV-probe experiments with asec resolutions.