The quantum entanglement dynamics of a one-dimensional spin-$1/2$ anisotropic $\mathit{XXZ}$ model is studied using the method of the adaptive time-dependent density-matrix renormalization group when two cases of quenches are performed in the system. An anisotropic interaction quench and the maximum number of domain walls of a staggered magnetization quench are considered. The dynamics of the pairwise entanglement between the nearest two qubits in the spin chain is investigated. The entanglement of the two spin qubits can be created and oscillates in both cases of the quench. The anisotropic interaction has a strong influence on the oscillation frequency of the entanglement.

Optical Sommerfeld-Brillouin precursors significantly ahead of a main field of comparable amplitude have been recently observed in an opaque medium with an electromagnetically induced transparency window [Wei et al., Phys. Rev. Lett. 103, 093602 (2009)]. We theoretically analyze in this article the somewhat similar results obtained when the transparency is induced by the propagating field itself and we establish an approximate analytic expression of the time delay of the main-field arrival, which fits fairly well the result obtained by numerically solving the Maxwell-Bloch equations.

Spin relaxation due to atom–atom collisions is measured for magnetically trapped erbium and thulium atoms at a temperature near 500 mK. The rate constants for Er–Er and Tm–Tm collisions are $3.0\times {10}^{-10}$ and $1.1\times {10}^{-10}$ cm${}^3$ ${\mathrm{s}}^{-1}$, respectively, $2–3$ orders of magnitude larger than those observed for highly magnetic $S$-state atoms. This is strong evidence for an additional, dominant, spin relaxation mechanism, electronic interaction anisotropy, in collisions between these “submerged-shell,” $L\ne 0$ atoms. These large spin relaxation rates imply that evaporative cooling of these atoms in a magnetic trap will be highly inefficient.

The ground-state phase diagram of mixtures of spin polarized fermions and bosons in a 1D periodic lattice is discussed in the limit of large fermion hopping and half filling of the fermions. Numerical simulations performed with the density matrix renormalization group (DMRG) show in addition to bosonic Mott insulating (MI), superfluid (SF), and charge density-wave phases (CDW) a yet unreported phase with spatial separation of MI and CDW regions. We derive an effective bosonic theory which allows for a complete understanding and quantitative prediction of the bosonic phase diagram. In particular the origin of CDW phase and the MI-CDW phase separation is revealed as an effective fermion-mediated long-range interaction between bosons with alternating sign.

We consider the general scenario of an excited level $|i\rangle$ of a quantum system that can decay via two channels: (i) via a single-quantum jump to an intermediate, resonant level $|\overline{m}\rangle$, followed by a second single-quantum jump to a final level $|f\rangle$, and (ii) via a two-quantum transition to a final level $|f\rangle$. Cascade processes $|i\rangle \to |\overline{m}\rangle \to |f\rangle$ and two-quantum transitions $|i\rangle \to |m\rangle \to |f\rangle$ compete (in the latter case, $|m\rangle$ can be both a nonresonant as well as a resonant level). General expressions are derived within second-order time-dependent perturbation theory, and the cascade contribution is identified. When the one-quantum decay rates of the virtual states are included into the complex resonance energies that enter the propagator denominator, it is found that the second-order decay rate contains the one-quantum decay rate of the initial state as a lower-order term. For atomic transitions, this implies that the differential-in-energy two-photon transition rate with complex resonance energies in the propagator denominators can be used to good accuracy even in the vicinity of resonance poles.

Assignment maps are mathematical operators that describe initial system-environment states for open quantum systems. We re-examine the notion of assignments that account for correlations between the system and the environment and show that these maps can be made linear at the expense of giving up positivity or consistency of the map. We study the role of positivity and consistency of the map and show the effects of relaxing these. Finally, we establish a connection between the violation of the positivity of linear assignments and the no-broadcasting theorem.

The weak convergence theorems of the one- and two-dimensional simple quantum walks, ${\mathrm{SQW}}^{(d)},d=1,2$, show a striking contrast to the classical counterparts, the simple random walks, ${\mathrm{SRW}}^{(d)}$. In the ${\mathrm{SRW}}^{(d)}$, the distribution of position $\mathbf{X}(t)$ of the particle starting from the origin converges to the Gaussian distribution in the diffusion scaling limit, in which the time scale $T$ and spatial scale $L$ both go to infinity as the ratio $L/\sqrt{T}$ is kept finite. On the other hand, in the ${\mathrm{SQW}}^{(d)}$, the ratio $L/T$ is kept to define the pseudovelocity $\mathbf{V}(t)=\mathbf{X}(t)/t$, and then all joint moments of the components $V_j(t),1⩽j⩽d$, of $\mathbf{V}(t)$ converge in the $T=L\to \infty$ limit. The limit distributions have novel structures such that they are inverted-bell shaped and their supports are bounded. In the present paper we claim that these properties of the ${\mathrm{SQW}}^{(d)}$ can be explained by the theory of relativistic quantum mechanics. We show that the Dirac equation with a proper ultraviolet cutoff can provide a quantum walk model in three dimensions, where the walker has a four-component qubit. We clarify that the pseudovelocity $\mathbf{V}(t)$ of the quantum walker, which solves the Dirac equation, is identified with the relativistic velocity. Since the quantum walker should be a tardyon, not a tachyon, $|\mathbf{V}(t)|<c$, where $c$ is the speed of light, and this restriction (the causality) is the origin of the finiteness of supports of the limit distributions universally found in quantum walk models. By reducing the number of components of momentum in the Dirac equation, we obtain the limit distributions of pseudovelocities for the lower dimensional quantum walks. We show that the obtained limit distributions for the one- and two-dimensional systems have common features with those of ${\mathrm{SQW}}^{(1)}$ and ${\mathrm{SQW}}^{(2)}$.

The x-ray resonant Raman scattering (RRS) effect of polarized and unpolarized radiation in the vicinity of the $1s$ absorption threshold of low-$Z$ elements such as magnesium, aluminum, and silicon is investigated. For the polarized and tunable exciting x-ray radiation the plane grating monochromator (PGM) beam line at the PTB laboratory in the BESSY II synchrotron radiation facility was employed, while unpolarized x-ray beams were induced by 1-MeV proton beam irradiation on various pure thick targets. For the latter case, a novel proton-induced x-ray fluorescence scattering chamber was designed and installed at the Tandem accelerator laboratory of the Institute of Nuclear Physics at N.C.S.R. “Demokritos.” The total RRS cross sections deduced from both independent excitation modes were found to be in a good agreement, within the experimental uncertainties. The predictions of the existing theory with respect to the dependence of the RRS to the incident beam polarization state is calculated and discussed with respect to the experimental results.

We analyze the repulsive fermionic Hubbard model on square and cubic lattices with spin imbalance and in the presence of a parabolic confinement. We analyze the magnetic structure as a function of the repulsive interaction strength and polarization. In the first part of the article, we perform unrestricted Hartree-Fock calculations for the two-dimensional (2D) case and find that above a critical interaction strength $U_c$ the system turns ferromagnetic at the edge of the trap, which is in agreement with the ferromagnetic Stoner instability of a homogeneous system away from half-filling. For $U<U_c$, we find a canted antiferromagnetic structure in the Mott region in the center and a partially polarized compressible edge. The antiferromagnetic order in the Mott plateau is perpendicular to the direction of the imbalance. In this regime, the same qualitative behavior is expected for 2D and three-dimensional (3D) systems. In the second part of the article, we give a general discussion of magnetic structures above $U_c$. We argue that spin conservation leads to nontrivial textures, both in the ferromagnetic polarization at the edge and for the Néel order in the Mott plateau. We discuss differences in magnetic structures for 2D and 3D cases.

We demonstrate the realization of a scheme for cold-atom gravimetry based on the recently demonstrated use of double-diffraction beam splitters [T. Lévèque, A. Gauguet, F. Michaud, F. Pereira Dos Santos, and A. Landragin, Phys. Rev. Lett. 103, 080405 (2009)], where the use of two retro-reflected Raman beams allows symmetric diffraction in $\pm \hslash k_{\mathrm{eff}}$ momenta. Although in principle restricted to the case of zero Doppler shift, for which the two pairs of Raman beams are simultaneously resonant, such diffraction pulses can remain efficient on atoms with nonzero velocity, such as in a gravimeter, when the frequency of one of the two Raman laser sources is modulated. Such pulses are used to realize an interferometer insensitive to laser phase noise and some of the dominant systematics. This approach reduces the technical requirements and would allow the realization of a simple atomic gravimeter. A sensitivity of $1.2\times {10}^{-7}g$ per shot is demonstrated.

We study the properties of an atom laser beam derived from a Bose-Einstein condensate using three different outcouplers, one based on multistate radio-frequency transitions and two others based on Raman transitions capable of imparting momentum to the beam. We first summarize the differences that arise in such systems, and how they may impact on the use of an atom laser in interferometry. Experimentally, we examine the formation of a bound state in all three outcouplers, a phenomenon which limits the atom laser flux, and find that a two-state Raman outcoupler is the preferred option for high-flux, low-divergence atom laser beams.

We study the matter-wave bistability in coupled atom-molecule quantum gases, in which heteronuclear molecules are created via an interspecies Feshbach resonance involving either two-species Bose or two-species Fermi atoms at zero temperature. We show that the resonant two-channel Bose model is equivalent to the nondegenerate parametric down-conversion in quantum optics, while the corresponding Fermi model can be mapped to a quantum optics model that describes a single-mode laser field interacting with an ensemble of inhomogeneously broadened two-level atoms. Using these analogies and the fact that both models are subject to the Kerr nonlinearity due to the two-body $s$-wave collisions, we show that under proper conditions, the population in the molecular state in both models can be made to change with the Feshbach detuning in a bistable fashion.

All experiments with ultracold atoms are performed in the presence of background residual gas. With the help of a suitable master equation we investigate a role of these fast atoms on the loss of coherence in optical lattices. We present an exact solution of the master equation and give the analytic formulas for all correlation functions in the presence of one-body losses. Additionally we discuss the existence of a Schrödinger cat state predicted in this system in Greiner et al. [Nature 419, 51 (2002)].

We study the compression of strong x-ray pulses from x-ray free-electron lasers (XFELs) propagating through the resonant medium of atomic argon. The simulations are based on the three-level model with the frequency of the incident x-ray pulse tuned in the $2p_{3/2}\text{−}4s$ resonance. The pulse propagation is accompanied by the self-seeded stimulated resonant Raman scattering (SRRS). The SRRS starts from two channels of amplified spontaneous emission (ASE), $4s\text{−}2p_{3/2}$ and $3s\text{−}2p_{3/2}$, which form the extensive ringing pattern and widen the power spectrum. The produced seed field triggers the Stokes ASE channel $3s\text{−}2p_{3/2}$. The population inversion is quenched for longer propagation distances where the ASE is followed by the lasing without inversion (LWI), which amplifies the Stokes component. Both ASE and LWI reshape the input pulse: The compressed front part of the pulse (up to 100 as) is followed by the long tail of the ringing and beating between the pump and Stokes frequencies. The pump pulse also generates weaker Stokes and anti-Stokes fields caused by four-wave mixing. These four spectral bands have fine structures caused by the dynamical Stark effect. A slowdown of the XFEL pulse up to 78% of the speed of light in vacuum is found because of a large nonlinear refractive index.

We investigate the possibility of using a hybrid coherent anti-Stokes Raman scattering technique for noninvasive monitoring of blood glucose levels. Our technique combines instantaneous coherent excitation of several characteristic molecular vibrations with subsequent probing of these vibrations by an optimally shaped, time-delayed, narrowband laser pulse. This pulse configuration mitigates the nonresonant four-wave mixing background while maximizing the Raman-resonant signal and allows rapid and highly specific detection even in the presence of multiple scattering. Under certain conditions we find that the measured signal is linearly proportional to the glucose concentration due to optical interference with the residual background light, which allows reliable detection of spectral signatures down to medically relevant glucose levels.

For a tripartite pure state of three qubits, it is well known that there are two inequivalent classes of genuine tripartite entanglement, namely the Greenberger-Horne-Zeilinger (GHZ) class and the W class. Any two states within the same class can be transformed into each other with stochastic local operations and classical communication with a nonzero probability. The optimal conversion probability, however, is only known for special cases. Here, lower and upper bounds are derived for the optimal probability of transformation from a GHZ state to other states of the GHZ class. A key idea in the derivation of the upper bounds is to consider the action of the local operations and classical communications (LOCC) protocol on a different input state, namely $1/\sqrt{2}[|000\rangle -|111\rangle ]$, and to demand that the probability of an outcome remains bounded by 1. We also find an upper bound for more general cases by using the constraints of the so-called interference term and 3-tangle. Moreover, some of the results are generalized to the case in which each party holds a higher dimensional system. In particular, the GHZ state generalized to three qutrits; that is, $|{\mathrm{GHZ}}_3\rangle =1/\sqrt{3}[|000\rangle +|111\rangle +|222\rangle ]$ shared among three parties can be transformed to any tripartite three-qubit pure state with probability 1 via LOCC. Some of our results can also be generalized to the case of a multipartite state shared by more than three parties.

It is known that at the critical point of a zero-temperature quantum phase transition in a one-dimensional spin system the entanglement entropy of a block of $L$ spins with the rest of the system scales logarithmically with $L$ with a prefactor determined by the central charge of the relevant conformal field theory. When we introduce critical slowing down incorporating the Kibble-Zurek mechanism of defect formation induced by a quench, the implicit nonadiabatic transition disturbs the scaling behavior. We have shown that in this case the entanglement entropy also obeys a scaling law such that it increases logarithmically with $L$ but the prefactor depends on the quench time. This puts a constraint on the block size $L$ so that we cannot arbitrarily choose it. Thus, the entanglement entropy obeys the scaling law only in a restrictive sense due to the formation of defects.

We study restrictions imposed by quantum mechanics on the process of matrix-element transfer. This problem is at the core of quantum measurements and state transfer. Given two systems $A$ and $B$ with initial density matrices $\lambda$ and $r$, respectively, we consider interactions that lead to transferring certain matrix elements of unknown $\lambda$ into those of the final state $\mathrm{r̃}$ of $B$. We find that this process eliminates the memory on the transferred (or certain other) matrix elements from the final state of $A$. If one diagonal matrix element is transferred, ${\mathrm{r̃}}_{\mathit{aa}}={\lambda }_{\mathit{aa}}$, the memory on each nondiagonal element ${\lambda }_{a\ne b}$ is completely eliminated from the final density operator of $A$. Consider the following three quantities, $\mathrm{Re}{\lambda }_{a\ne b}$, $\mathrm{Im}{\lambda }_{a\ne b}$, and ${\lambda }_{\mathit{aa}}-{\lambda }_{\mathit{bb}}$ (the real and imaginary part of a nondiagonal element and the corresponding difference between diagonal elements). Transferring one of them, e.g., $\mathrm{Re}{\mathrm{r̃}}_{a\ne b}=\mathrm{Re}{\lambda }_{a\ne b}$, erases the memory on two others from the final state of $A$. Generalization of these setups to a finite-accuracy transfer brings in a trade-off between the accuracy and the amount of preserved memory. This trade-off is expressed via system-independent uncertainty relations that account for local aspects of the accuracy-disturbance trade-off in quantum measurements. Thus, the general aspect of state disturbance in quantum measurements is elimination of memory on non-diagonal elements, rather than diagonalization.