Geometric phase of mixed state for three-level open system is defined by establishing in connecting density matrix with nonunit vector ray in a three-dimensional complex Hilbert space. Because the geometric phase depends only on the smooth curve on this space, it is formulated entirely in terms of geometric structures. Under the limiting of pure state, our approach is in agreement with the Berry phase, Pantcharatnam phase, and Aharonov and Anandan phase. We find that, furthermore, the Berry phase of mixed state correlated to population inversions of three-level open system.

We present a measurement of the dynamic scalar and tensor polarizabilities of the excited state $|5d6s\hspace{0.5em}{}^3{D}_1\rangle$ in atomic ytterbium. The polarizabilities were measured by analyzing the spectral lineshape of the 408-nm $6s^2\hspace{0.5em}{}^1{S}_0\to 5d6s\hspace{0.5em}{}^3{D}_1$ transition driven by a standing wave of resonant light in the presence of static electric and magnetic fields. Due to the interaction of atoms with the standing wave, the lineshape has a characteristic polarizability-dependent distortion. A theoretical model was used to simulate the lineshape and determine a combination of the polarizabilities of the ground and excited states by fitting the model to experimental data. This combination was measured with a 13$\%$ uncertainty, only 3$\%$ of which was due to uncertainty in the simulation and fitting procedure. By comparing two different combinations of polarizabilities, the scalar and tensor polarizabilities of the state $|5d6s\hspace{0.5em}{}^3{D}_1\rangle$ were measured to be ${\alpha }_0({}^3{D}_1)=0.009(21)\hspace{0.5em}{\mathrm{Hz}(\mathrm{V}/\mathrm{cm})}^{-2}$ and ${\alpha }_2({}^3{D}_1)=-0.103(26)\hspace{0.5em}\mathrm{Hz}(\mathrm{V}/\mathrm{cm}){}^{-2}$, respectively. We show that this technique can be applied to similar atomic systems.

We study the use of an optical Feshbach resonance to modify the $p$-wave interaction between ultracold polarized ${}^{171}\mathrm{Yb}$ spin-$1/2$ fermions. A laser exciting two colliding atoms to the ${}^1{S}_0+{}^3{P}_1$ channel can be detuned near a purely-long-range excited molecular bound state. Such an exotic molecule has an inner turning point far from the chemical binding region, and thus, three-body recombination in the Feshbach resonance will be highly suppressed in contrast to that typically seen in a ground-state $p$-wave magnetic Feshbach resonance. We calculate the excited molecular bound-state spectrum using a multichannel integration of the Schrödinger equation, including an external perturbation by a magnetic field. From the multichannel wave functions, we calculate the Feshbach resonance properties, including the modification of the elastic $p$-wave scattering volume and inelastic spontaneous scattering rate. The use of magnetic fields and selection rules for polarized light yields a highly controllable system. We apply this control to propose a toy model for three-color superfluidity in an optical lattice for spin-polarized ${}^{171}\mathrm{Yb}$, where the three colors correspond to the three spatial orbitals of the first excited $p$ band. We calculate the conditions under which tunneling and on-site interactions are comparable, at which point quantum critical behavior is possible.

Angular distribution and spectral ($e$,$2$$e$) measurements are reported for the helium autoionizing levels $(2s^2){}^{1}S$, $(2p^2){}^{1}D$, and $(2s2p){}^{1}P$. A special out-of-plane geometry is used where the ejected electrons are emitted in a plane perpendicular to the scattered electron direction. The kinematics are chosen so that this plane contains the momentum-transfer direction. While the recoil peak almost vanishes in the angular distribution for direct ionization, it remains significant for the autoionizing levels and exhibits a characteristic shape for each orbital angular momentum $L=0,1,2$. A second-order model in the projectile-target interaction correctly reproduces the observed magnitudes of the recoil peaks, but is a factor of 2 too large in the central out-of-plane region. Observed ($e$,2$e$) energy spectra for the three resonances over the full angular range are well reproduced by the second-order calculation. Calculations using a first-order model fail to reproduce both the magnitudes of the recoil peaks and the spectral line profiles.

The nature of a few low-lying laser-induced resonances of HD${}^{+}$ along with their linewidths due to dissociation, has been investigated in the intensity range of (1–6) $\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ for three different laser frequencies. In the length gauge representation of the interaction Hamiltonian used by us, these resonances for the lower intensities are basically the vibrational states of the unperturbed molecule, shifted and broadened by radiative interactions. At higher intensities the resonances are obtained as quasistationary states on different adiabatic potentials. They are formed by the mixing of various unperturbed vibrational states by multiphoton interactions. In this mixing, the proportion of vibrational states further away from the resonance energy increases with the increase in intensity. At high enough intensities, signature of dissociation through a nonresonant intermediate vibrational transition to the $v=6$ and $v=7$ state is observed for a laser frequency of 12 500 cm${}^{-1}$. The width of the lowest resonance increases sharply with intensity, while its shift from the $v=0$ state increases only linearly with intensity. The branching ratios to different photon absorption channels change with intensity and they can be interpreted using the adiabatic potential curves. For a frequency of 2000 cm${}^{-1}$, which is close to the frequency of $v=0$ to $v=1$ transition, the resonances arise from the mixing of various vibrational levels through stepwise transitions, resulting in a dissociation linewidth larger compared to that obtained for higher frequencies.

We discuss the creation of nonclassical light from collective atomic states that are prepared in a ring-shaped lattice. These states are realized by exploiting the strong interaction between atoms in high-lying energy levels—the so-called Rydberg states—and yield a resource for creating excitations of the electromagnetic field that carry few photons. We characterize the properties of these photonic states showing that they are determined by the interplay among the ring geometry, the structure of the atomic resource states, and the collectivity in the photon emission which is controlled by the lattice spacing. The system permits the creation of versatile single-photon sources and two-photon entangled states.

Two species superfluid Fermi gas is investigated on the BCS side up to the Feshbach resonance. Using the Greens’s function technique gradient corrections are calculated to the generalized Thomas-Fermi theory including Cooper pairing. Their relative magnitude is found to be measured by the small parameter $(d/R_{\mathrm{TF}}){}^4$, where $d$ is the oscillator length of the trap potential and $R_{\mathrm{TF}}$ is the radial extension of the density $n$ in the Thomas-Fermi approximation. In particular, at the Feshbach resonance the universal corrections to the local density approximation are calculated and a universal prefactor ${\kappa }_W=7/27$ is derived for the von Weizsäcker–type correction ${\kappa }_W(\hslash {}^2/2m)({\nabla }^2{n}^{1/2}/n^{1/2})$.

The isotropic scattering phase shift is calculated for nonrelativistic bosons interacting at low energies via an arbitrary finite-range potential in $d$ space-time dimensions. Scattering on a $(d-1)$-dimensional torus is then considered, and the eigenvalue equation relating the energy levels on the torus to the scattering phase shift is derived. With this technology in hand, and focusing on the case of two spatial dimensions, a perturbative expansion is developed for the ground-state energy of $N$ identical bosons which interact via an arbitrary finite-range potential in a finite area. The leading nonuniversal effects due to range corrections and three-body forces are included. It is then shown that the thermodynamic limit of the ground-state energy in a finite area can be taken in closed form to obtain the energy per particle in the low-density expansion by explicitly summing the parts of the finite-area energy that diverge with powers of $N$. The leading and subleading finite-size corrections to the thermodynamic limit equation of state are also computed. Closed-form results—some well known, others perhaps not—for two-dimensional lattice sums are included in an Appendix.

We describe an experimental setup and the cooling procedure for producing ${}^{39}\mathrm{K}$ Bose-Einstein condensates of over $4\times {10}^5$ atoms. Condensation is achieved via a combination of sympathetic cooling with ${}^{87}\mathrm{Rb}$ in a quadrupole-Ioffe-configuration (QUIC) magnetic trap and direct evaporation in a large-volume crossed optical dipole trap, where we exploit the broad Feshbach resonance at 402 G to tune the ${}^{39}\mathrm{K}$ interactions from weak and attractive to strong and repulsive. In the same apparatus we create quasipure ${}^{87}\mathrm{Rb}$ condensates of over $8\times {10}^5$ atoms.

The analysis of the statistical properties of the point process (PP) of photon detection times can be used to determine whether or not an optical field is classical, in the sense that its statistical description does not require the methods of quantum optics. This determination is, however, more difficult than ordinarily admitted and the first aim of this paper is to illustrate this point by using some results of the PP theory. For example, it is well known that the analysis of the photodetection of classical fields exhibits the so-called bunching effect. But this property alone cannot be used to decide the nature of a given optical field. Indeed, we have presented examples of point processes for which a bunching effect appears and yet they cannot be obtained from a classical field. These examples are illustrated by computer simulations. Similarly, it is often admitted that for fields with very low light intensity the bunching or antibunching can be described by using the statistical properties of the distance between successive events of the point process, which simplifies the experimental procedure. We have shown that, while this property is valid for classical PPs, it has no reason to be true for nonclassical PPs, and we have presented some examples of this situation also illustrated by computer simulations.

We propose a procedure to fully reconstruct the time-dependent coefficients of convolutionless non-Markovian dissipative generators via a finite number of experimental measurements. By combining a tomography-based approach with a proper data sampling, our proposal allows to relate the time-dependent coefficients governing the dissipative evolution of a quantum system to experimentally accessible quantities. The proposed scheme not only provides a way to retrieve the full information about potentially unknown dissipative coefficients, but also, most valuably, can be employed as a reliable consistency test for the approximations involved in the theoretical derivation of a given non-Markovian convolutionless master equation.

Based on the mean-field approximation and a phase-space analysis, we discuss the dynamics of Bose-Einstein condensates (BECs) in a double-well potential. The condensates are found to be trapped in the time-dependent eigenstates of the effective Hamiltonian; we refer to this effect as time-dependent self-trapping of BECs. By comparison of this self-trapping with the adiabatic evolution, we find that adiabatic evolution beyond the traditional adiabatic condition can be achieved in BECs. Furthermore, the population imbalance of the BECs in the wells can be controlled by manipulating the atom-atom couplings and the driving field. The fixed points for the system are also calculated and discussed.

We study the spatial decoherence dynamics for the relative position of two atoms in a single-mode ring cavity. We find that the spatial decoherence of the two atoms depends strongly on their relative position. Taking into account the spatial degrees of freedom, we investigate the entanglement dynamics of the internal states of the two atoms. It is shown that the entanglement decays to almost zero in a finite time, and the disentanglement time depends on the width of the wave packets describing the atomic spatial distribution.

Radiation pressure affects the kinetics of a system exposed to radiation and it constitutes the basis of laser cooling. In this article, we study matter-wave pressure through examining the dynamics of a quantum-classical hybrid system. The quantum and classical subsystems are affected mutually via a changing boundary condition. Two systems, that is, an atom and a Bose-Einstein condensate (BEC), are considered as the quantum subsystems, while an oscillating wall is taken as the classical subsystem. We show that the classical subsystem would experience a force proportional to $Q^{-3}$ from the quantum atom, where $Q$ denotes the distance between the two walls, whereas it acquires an additional force proportional to $Q^{-2}$ from the BEC due to the atom-atom interaction in the BEC. These forces can be understood as the matter-wave pressure.

We analyze the fundamental security significance of the quantitative criteria on the final generated key $K$ in quantum key generation including the quantum criterion $d$, the attacker’s mutual information on $K$, and the statistical distance between her distribution on $K$ and the uniform distribution. For operational significance a criterion has to produce a guarantee on the attacker’s probability of correctly estimating some portions of $K$ from her measurement, in particular her maximum probability of identifying the whole $K$. We distinguish between the raw security of $K$ when the attacker just gets at $K$ before it is used in a cryptographic context and its composition security when the attacker may gain further information during its actual use to help get at $K$. We compare both of these securities of $K$ to those obtainable from conventional key expansion with a symmetric key cipher. It is pointed out that a common belief in the superior security of a quantum generated $K$ is based on an incorrect interpretation of $d$ which cannot be true, and the security significance of $d$ is uncertain. Generally, the quantum key distribution key $K$ has no composition security guarantee and its raw security guarantee from concrete protocols is worse than that of conventional ciphers. Furthermore, for both raw and composition security there is an exponential catch-up problem that would make it difficult to quantitatively improve the security of $K$ in a realistic protocol. Some possible ways to deal with the situation are suggested.

We address the problem of the information-disturbance tradeoff associated to the estimation of a quantum transformation and show how the extraction of information about a black box causes a perturbation of the corresponding input-output evolution. In the case of a black box performing a unitary transformation, randomly distributed according to the invariant measure, we give a complete solution of the problem, deriving the optimal tradeoff curve and presenting an explicit construction of the optimal quantum network.

Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system’s ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures, to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected. We also classify distinct operational criteria for preservation (e.g., “noiseless,” “unitarily correctible,” etc.) and introduce two natural criteria for measurement-stabilized and unconditionally preserved codes. Finally, for several of these operational criteria, we present efficient (polynomial in the state-space dimension) algorithms to find all of a channel’s information-preserving structures.

In the research presented here, we reconsider the problem of obtaining stable resonant features in linear absorption spectroscopy, which has application to ultraminiature atomic physics where sub-Doppler spectroscopic techniques are not always optimal. In particular, we consider the applicability of isoclinic points for precision atomic spectroscopy. These are defined as “[a] wavelength, wave number, or frequency at which the first derivative of an absorption spectrum of a sample does not change upon a chemical reaction or physical change of the sample,” and we demonstrate the existence of isoclinic points in the $D_1$ spectra of $I=3/2$ alkali-metal isotopes, where $I$ is the nuclear spin. We then consider the $D_1$ isoclinic point of ${}^{87}\mathrm{Rb}$ in detail, showing that a slight ${}^{85}\mathrm{Rb}$ contamination in real ${}^{87}\mathrm{Rb}$ samples should have no significant effect on the frequency stability of the isoclinic point and that optical pumping by a linearly polarized laser should also not affect the isoclinic point’s stability (i.e., the isoclinic point is insensitive to laser intensity). Finally, we perform an experiment demonstrating that the ${}^{87}\mathrm{Rb}$ $D_1$ isoclinic point has a temperature shift more than an order of magnitude smaller than that of the most isolated transition in the ${}^{87}\mathrm{Rb}$ $D_1$ spectrum.

We determine the energy-level shift experienced by a neutral atom due the quantum electromagnetic interaction with a layered dielectric body. We use the technique of normal-mode expansion to quantize the electromagnetic field in the presence of a layered, nondispersive, and nonabsorptive dielectric. We explicitly calculate the equal-time commutation relations between the electric field and vector potential operators. We show that the commutator can be expressed in terms of a generalized transverse $\delta$ function and that this is a consequence of using the generalized Coulomb gauge to quantize the electromagnetic field. These mathematical tools turn out to be very helpful in the calculation of the energy-level shift of the atom, which can be in its ground state or excited. The results for the shift are then analyzed asymptotically in various regions of the system’s parameter space, with a view to providing quick estimates of the influence of a single dielectric layer on the Casimir-Polder interaction between an atom and a dielectric half space. We also investigate the impact of resonances between the wavelength of the atomic transition and the thickness of the top layer.