We investigate the decay of initial states that possess a tail that extends beyond the interaction potential region, for potentials of arbitrary shape that vanish exactly after a distance. This is the case for a relevant class of artificial quantum structures. We obtain that along the internal interaction region, the time evolution of the decaying wave function is formed by two terms. The first one refers to the proper decay of the internal portion of the initial state, whereas the second one, that arises from the external tail, yields a transient contribution that tunnels into the internal region, builds up to a value, and then decays. We obtain that depending on the parameters of the initial state, the nonexponential tail decaying contribution may be larger than the contribution of the proper nonexponential term. These results are illustrated by an exactly solvable model and the Heidelberg potential for decay of ultracold atoms and open the possibility to control initial states in artificial decaying systems.

Tunneling times in atomic ionization are studied theoretically by a virtual detector approach. A virtual detector is a hypothetical device that allows one to monitor the wave function's density with spatial and temporal resolution during the ionization process. With this theoretical approach, it becomes possible to define unique moments when the electron enters and leaves with highest probability the classically forbidden region from first principles and a tunneling time can be specified unambiguously. It is shown that neither the moment when the electron enters the tunneling barrier nor when it leaves the tunneling barrier coincides with the moment when the external electric field reaches its maximum. Under the tunneling barrier as well as at the exit the electron has a nonzero velocity in the electric field direction. This nonzero exit velocity has to be incorporated when the free motion of the electron is modeled by classical equations of motion.

Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes the structure of the graph causes the walker to get trapped, such that the probability of finding the marked vertex is limited. We give an example with two linked cliques, proving that the captive probability can be liberated by increasing the weights of the links. This allows the search to succeed with probability 1 without increasing the energy scaling of the algorithm. Further increasing the weights, however, slows the runtime, so the optimal search requires weights that are neither too weak nor too strong.

One-dimensional spinor gases with strong $\delta$ interaction fermionize and form a spin chain. The spatial degrees of freedom of this atom chain can be described by a mapping to spinless noninteracting fermions and the spin degrees of freedom are described by a spin-chain model with nearest-neighbor interactions. Here, we compute momentum and occupation-number distributions of up to 16 strongly interacting spinor fermions and bosons as a function of their spin imbalance, the strength of an externally applied magnetic field gradient, the length of their spin, and for different excited states of the multiplet. We show that the ground-state momentum distributions resemble those of the corresponding noninteracting systems, apart from flat background distributions, which extend to high momenta. Moreover, we show that the spin order of the spin chain—in particular antiferromagnetic spin order—may be deduced from the momentum and occupation-number distributions of the system. Finally, we present efficient numerical methods for the calculation of the single-particle densities and one-body density matrix elements and of the local exchange coefficients of the spin chain for large systems containing more than 20 strongly interacting particles in arbitrary confining potentials.

Microscopic silicon-based suspended mechanical oscillators, constituting an extremely sensitive force probe, transducer, and actuator, are being increasingly employed in many developing microscopies, spectroscopies, and emerging optomechanical and chem-bio sensors. We predict a significant squeezing in the quantum state of motion of an oscillator constrained as a beam and subject to an electrically induced nonlinearity. By taking into account the quantum noise, the underlying nonlinear dynamics is investigated in both the transient and stationary regimes of the driving force leading to the finding that strongly squeezed states are accessible in the vicinity of the pull-in instability of the oscillator. We discuss a possible application of this strong quantum squeezing as an optomechanical method for detecting broad-spectrum single or low-count photons, and further suggest other novel sensing actions.

We propose to understand surface-enhanced Raman scattering (SERS) as a higher-order Raman process that contains the plasmonic excitation. The SERS amplitudes are calculated with third- and fourth-order perturbation theory. Treating the plasmonic excitation as a quasiparticle, we derive analytic expressions for all coupling matrix elements. This leads to a general theory of plasmonic enhancement in SERS that can be applied to arbitrary plasmonic nanostructures. We obtain the plasmon eigenvectors of a gold nanosphere and a nanosphere dimer. They are used to calculate the enhancement of the Raman cross section of a molecule coupled to the dipole plasmon mode. The enhancement of the cross section is up to three orders of magnitude stronger than predicted by the theory of electromagnetic enhancement. The difference is most pronounced in vacuum and decreases with increasing dielectric constant of the embedding medium. The predictions from understanding SERS as a higher-order Raman process agree well with recent experiments; they highlight the dominance of plasmonic enhancement in SERS.

The Green's function formalism is used in order to model the diffusion of free carriers in nonlinear semiconductor nanoscale resonators. In combination with the time-dependent coupled-mode equations, this leads to excellent agreement with measurements carried on a variety of samples and materials, using a minimal set of fitting parameters. The role of the geometry of the cavity is evidenced and the influence of linear and nonlinear absorption on the response of the resonator is discussed. This model can handle a broad range of phenomena: switching, self-pulsing, including resonant four-wave mixing.

We use a momentum-space hole-burning technique implemented via stimulated Raman transitions to measure the momentum relaxation time for a gas of bosonic atoms trapped in an optical lattice. By changing the lattice potential depth, we observe a smooth crossover between relaxation times larger and smaller than the bandwidth. The latter condition violates the Mott-Ioffe-Regel bound and indicates a breakdown of the quasiparticle picture. We produce a simple kinetic model that quantitatively predicts these relaxation times. Finally, we introduce a cooling technique based upon our hole-burning technique.

We extend the non-Hermitian one-dimensional quantum walk model [Phys. Rev. Lett. 102, 065703 (2009)] by taking the dephasing effect into account. We prove that the feature of topological transition does not change even when dephasing between the sites within units is present. The potential experimental observation of our theoretical results in the circuit QED system consisting of superconducting qubit coupled to a superconducting resonator mode is discussed and numerically simulated. The results clearly show a topological transition in quantum walk and display the robustness of such a system to the decay and dephasing of qubits. We also discuss how to extend this model to higher dimension in the circuit QED system.

We investigate the possibility of achieving high-fidelity universal two-qubit gates by supplementing optimal tuning of individual qubits with dynamical decoupling (DD) of local $1/f$ noise. We consider simultaneous local pulse sequences applied during the gate operation and compare the efficiencies of periodic, Carr-Purcell, and Uhrig DD with hard $\pi$ pulses along two directions (${\pi }_{z/y}$ pulses). We present analytical perturbative results (Magnus expansion) in the quasistatic noise approximation combined with numerical simulations for realistic $1/f$ noise spectra. The gate efficiency is studied as a function of the gate duration, of the number $n$ of pulses, and of the high-frequency roll-off. We find that the gate error is nonmonotonic in $n$, decreasing as $n^{-\alpha }$ in the asymptotic limit, $\alpha \ge 2$, depending on the DD sequence. In this limit ${\pi }_z$-Urhig is the most efficient scheme for quasistatic $1/f$ noise, but it is highly sensitive to the soft UV cutoff. For small number of pulses, ${\pi }_z$ control yields anti-Zeno behavior, whereas ${\pi }_y$ pulses minimize the error for a finite $n$. For the current noise figures in superconducting qubits, two-qubit gate errors $\sim {10}^{-6}$, meeting the requirements for fault-tolerant quantum computation, can be achieved. The Carr-Purcell-Meiboom-Gill sequence is the most efficient procedure, stable for $1/f$ noise with UV cutoff up to gigahertz.

We report on the creation of ultracold heteronuclear and electronically excited Rb*Yb molecules in a hybrid conservative trap by photoassociation of ultracold ${}^{87}\mathrm{Rb}$ and ${}^{176}\mathrm{Yb}$. The molecules are formed below the ${\mathrm{Rb}}_{5\mathit{p}1}\left({}^{2}P_{1/2}\right)+{\mathrm{Yb}}_{6\mathit{s}2}({}^{1}S_0)$ dissociation limit and the resonances are detected using trap-loss spectroscopy. By addressing vibrational levels with binding energies down to $E_B=-h\times 2.2\mathrm{THz}$, we study the change in hyperfine coupling of the diatomic molecule as a function of internuclear separation. We observe a decreasing hyperfine splitting for more tightly bound excited molecular states where the hyperfine splitting is reduced by more than $30\%$ compared to the atomic value for ${}^{87}\mathrm{Rb}$.

We theoretically verify that the symmetry breaking in spherical resonators can result in a fractal frequency spectrum that is full of numerous new accidental degeneracies to cluster around the unperturbed degenerate cavity. We further experimentally discover that the fractal frequency spectrum excellently reflects the intimate connection between the emission power and the degenerate mode numbers. It is observed that the wave distributions of lasing modes at the accidental degeneracies are strongly concentrated on three-dimensional (3D) geometric topology. Considering the overlapping effect, the wave representation of the coherent states is analytically derived to manifest the observed 3D geometric surfaces.

We report on detailed studies of electronic and nuclear spin states in the diamond-nitrogen-vacancy (NV) center under weak transverse magnetic fields. We numerically predict and experimentally verify a previously unobserved NV hyperfine level anticrossing (LAC) occurring at bias fields of tens of gauss—two orders of magnitude lower than previously reported LACs at $\sim 500$ and $\sim 1000$ G axial magnetic fields. We then discuss how the NV ground-state Hamiltonian can be manipulated in this regime to tailor the NV's sensitivity to environmental factors and to map into the nuclear spin state.

Spectral line shapes are sensitive to plasma conditions and are often used to diagnose electron density of laboratory plasmas as well as astrophysical plasmas. Stark line-shape models take into account the perturbation of the radiator's energy structure due to the Coulomb interaction with the surrounding charged particles. Solving this Coulomb interaction is challenging and is commonly approximated via a multipole expansion. However, most models include only up to the second term of the expansion (the dipole term). While there have been studies on the higher-order terms due to one of the species (i.e., either ions or electrons), there is no model that includes the terms beyond dipole from both species. Here, we investigate the importance of the higher-order multipole terms from both species on the $\mathrm{H}\beta$ line shape. First, we find that it is important to include higher-order terms consistently from both ions and electrons to reproduce measured line-shape asymmetry. Next, we find that the line shape calculated with the dipole-only approximation becomes inaccurate as density increases. It is necessary to include up to the third (quadrupole) term to compute the line shape accurately within 2%. Since most existing models include only up to the dipole terms, the densities inferred with such models are in question. We find that the model without the quadrupole term slightly underestimates the density, and the discrepancy becomes as large as 12% at high densities. While the case of study is limited to $\mathrm{H}\beta$, we expect similar impact on other lines.

We develop a simple numerical method that allows us to calculate the BCS superfluid transition temperature $T_c$ precisely for any interaction potential. We apply it to a polarized, ultracold Fermi gas with long-range, anisotropic, dipolar interactions and include the effects of anisotropic exchange interactions. We pay particular attention to the short-range behavior of dipolar gases and reexamine current renormalization methods. In particular, we find that dimerization of both atoms and molecules significantly hampers the formation of a superfluid. The end result is that at high density or interaction strengths, we find $T_c$ is orders of magnitude lower than previous calculations.

We investigate the wave-packet dynamics of a pair of particles that undergoes a rapid change of scattering length. The short-range interactions are modeled in the zero-range limit, where the quench is accomplished by switching the boundary condition of the wave function at vanishing particle separation. This generates a correlation wave that propagates rapidly to nonzero particle separations. We have derived universal, analytic results for this process that lead to a simple phase-space picture of the quench-induced scattering. Intuitively, the strength of the correlation wave relates to the initial contact of the system. We find that, in one spatial dimension, the $k^{-4}$ tail of the momentum distribution contains a ballistic contribution that does not originate from short-range pair correlations, and a similar conclusion can hold in other dimensionalities depending on the quench protocol. We examine the resultant quench-induced transport in an optical lattice in one dimension, and a semiclassical treatment is found to give quantitatively accurate estimates for the transport probabilities.

We consider quantum phases of tightly confined spin-2 bosons in an external field under the presence of rotationally invariant interactions. Generalizing previous treatments, we show how this system can be mapped onto a quantum rotor model. Within the rotor framework, low-energy excitations about fragmented states, which cannot be accessed within standard Bogoliubov theory, can be obtained. In the spatially extended system in the thermodynamic limit there exists a mean field ground-state degeneracy between a family of nematic states for appropriate interaction parameters. It has been established that quantum fluctuations lift this degeneracy through the mechanism of order by disorder and select either a uniaxial or square-biaxial ground state. On the other hand, in the full quantum treatment of the analogous single-spatial-mode problem with finite-particle number, it is known that, due to symmetry-restoring fluctuations, there is a unique ground state across the entire nematic region of the phase diagram. Within the established rotor framework, we investigate the possible quantum phases under the presence of a quadratic Zeeman field, a problem which has previously received little attention. By investigating wave-function overlaps, we do not find any signatures of the order-by-disorder phenomenon which is present in the continuum case. Motivated by this, we consider an alternative external potential which breaks less symmetry than the quadratic Zeeman field. For this case, we do find the phenomenon of order by disorder in the fully quantum system. This is established within the rotor framework and with exact diagonalization.