A harmonically trapped ultracold 1D spinor Fermi gas with a strongly attractive 1D even-wave interaction induced by a 3D Feshbach resonance is studied. It is shown that it has two different super Tonks-Girardeau (sTG) energy eigenstates which are metastable against collapse in spite of the strong attraction, due to their close connection with 1D hard sphere Bose gases which are highly excited gaslike states. One of these sTG states is a hybrid between an sTG gas with strong $(\uparrow \downarrow )$ attractions and an ideal Fermi gas with no $(\uparrow \uparrow )$ or $(\downarrow \downarrow )$ interactions, the sTG component being an exact analog of the recently observed sTG state of a 1D ultracold Bose gas. It should be possible to create it experimentally by a sudden switch of the $(\uparrow \downarrow )$ interaction from strongly repulsive to strongly attractive, as in the recent Innsbruck experiment on the bosonic sTG gas. The other is a trapped analog of a recently predicted sTG state which is an ultracold gas of strongly bound $(\uparrow \downarrow )$ fermion dimers which behave as bosons with a strongly attractive boson-boson interaction leading to sTG behavior. It is proved that the probability of a transition from the ground state for strongly repulsive interaction to this dimer state under a sudden switch from strongly repulsive to strongly attractive interaction is $\ll$$1$, contrary to a previous suggestion.

We report on the attainment of a spin-polarized Fermi sea of ${}^{87}\mathrm{Sr}$ in thermal contact with a Bose-Einstein condensate (BEC) of ${}^{84}\mathrm{Sr}$. Interisotope collisions thermalize the fermions with the bosons during evaporative cooling. A degeneracy with $T/T_F=0.30(5)$ is reached for a ${}^{87}\mathrm{Sr}$ Fermi sea of $2\times {10}^4$ atoms together with an almost pure ${}^{84}\mathrm{Sr}$ BEC of ${10}^5$ atoms.

We elucidate the geometry of quantum adiabatic evolution. By minimizing the deviation from adiabaticity, we find a Riemannian metric tensor underlying adiabatic evolution. Equipped with this tensor, we identify a unified geometric description of quantum adiabatic evolution and quantum phase transitions that generalizes previous treatments to allow for degeneracy. The same structure is relevant for applications in quantum information processing, including adiabatic and holonomic quantum computing, where geodesics over the manifold of control parameters correspond to paths which minimize errors. We illustrate this geometric structure with examples, for which we explicitly find adiabatic geodesics. By solving the geodesic equations in the vicinity of a quantum critical point, we identify universal characteristics of optimal adiabatic passage through a quantum phase transition. In particular, we show that in the vicinity of a critical point describing a second-order quantum phase transition, the geodesic exhibits power-law scaling with an exponent given by twice the inverse of the product of the spatial and scaling dimensions.

We develop a series of resonant short-range two-boson potentials reproducing the same two-body low-energy observables and apply them in three- and four-body calculations. We demonstrate that the universal behavior predicted by effective field theory may be strongly violated and analyze the conditions for this phenomenon.

We investigate the coherent control of nonresonant two-photon excitation and ($2+1$) photon ionization processes from the time-dependent perspective. To this end, we have solved the time-dependent Schrödinger equation for a hydrogen atom interacting with an ultraviolet laser field. Results are obtained for symmetric and antisymmetric phase distributions leading to dark and bright pulses, for which the temporal field distributions consist of many subpulses. For the two-photon excitation process, it is found that at intermediate time between the subpulses, the population in the excited state can exceed the final state population and, in particular, is nonzero for dark pulses. The results for the ($2+1$) photon ionization closely follow those for the excitation process, which shows that the ionization of the electron proceeds as a resonant process via the excited state in all cases considered.

We analyze the simultaneous time-optimal control of two-spin systems. The two noncoupled spins, which differ in the value of their chemical offsets, are controlled by the same magnetic fields. Using an appropriate rotating frame, we restrict the study to the case of opposite shifts. We then show that the optimal solution of the inversion problem in a rotating frame is composed of a pulse sequence of maximum intensity and is similar to the optimal solution for inverting only one spin by using a nonresonant control field in the laboratory frame. An example is implemented experimentally using nuclear magnetic resonance techniques.

An easily scalable toroidal geometry presents an opportunity for creating large-scale persistent currents in Bose-Einstein condensates, for studies of the Kibble-Zurek mechanism, and for investigations of toroidally trapped degenerate Fermi gases. We consider in detail the process of isentropic loading of a Bose or Fermi gas from a harmonic trap into the scale-invariant toroidal regime that exhibits a high degree of system invariance when increasing the radius of the toroid. The heating involved in loading a Bose gas is evaluated analytically and numerically, both above and below the critical temperature. Our numerical calculations treat interactions within the Hartree-Fock-Bogoliubov-Popov theory. Minimal change in degeneracy is observed over a wide range of initial temperatures, and a regime of cooling is identified. The scale-invariant property is further investigated analytically by studying the density of states of the system, revealing the robust nature of scale invariance in this trap, for both bosons and fermions. We give analytical results for a Thomas-Fermi treatment. We calculate the heating due to loading a spin-polarized Fermi gas and compare with analytical results for high- and low-temperature regimes. The Fermi gas is subjected to irreducible heating during loading, caused by the loss of one degree of freedom for thermalization.

We present a potential scheme to entangle negatively charged nitrogen-vacancy (N-$V$) centers in distance using nanomechanical resonators (NAMRs) and a common superconducting quantum interference device (SQUID). By virtually exciting the vibrational modes of the NAMRs, we show the effective coupling between the N-$V$ centers and the SQUID, which is a promising step toward large-sized quantum-information processing with separate N-$V$ centers.

The role of spontaneous emission in the interaction between a two-level atom and a pumped microcavity in the strong-coupling regime is discussed. In particular, using a quantum Monte Carlo simulation, we investigate atomic spatial coherence. It is found that atomic spontaneous emission destroys the coherence between neighboring lattice sites, while cavity decay does not. Furthermore, our computation of the spatial coherence function shows that the in-site locality is little affected by the cavity decay but greatly depends on the cavity pump amplitude.

I show that in tomographic experiments, the measurement of a small set of observables suffices to confirm or incrementally amend prior expectations with a high degree of confidence. To this end, I adapt the evidence procedure, an estimation technique used in classical image reconstruction, for use in quantum-state tomography.

Some of the asymmetric three-qubit $W$ states are used for perfect teleportation, superdense coding, and quantum-information splitting. We present the protocols for the optimal distillation of the asymmetric as well as the symmetric $W$ states from a single copy of any three-qubit $W$ class pure state.

We investigate chains of $d$-dimensional quantum spins (qudits) on a line with generic nearest-neighbor interactions without translational invariance. We find the conditions under which these systems are not frustrated, that is, when the ground states are also the common ground states of all the local terms in the Hamiltonians. The states of a quantum spin chain are naturally represented in the matrix product states (MPS) framework. Using imaginary time evolution in the MPS ansatz, we numerically investigate the range of parameters in which we expect the ground states to be highly entangled and find them hard to approximate using our MPS method.

The correction of errors is of fundamental importance for the development of contemporary computing devices and robust communication protocols. In this paper we propose a scheme for the implementation of the three-qubit quantum repetition code, exploiting the interaction of Rydberg atoms with the quantized mode of a microwave cavity field. Quantum information is encoded within two circular Rydberg states of the atoms and encoding and decoding processes are realized within two separate microwave cavities. We show that errors due to phase-noise fluctuations could be efficiently corrected using a state-of-the-art apparatus.

A simple method for implementing an asymmetrical two-dimensional magnetic lattice is proposed. The asymmetrical two-dimensional magnetic lattice is created by periodically distributing nonzero magnetic minima across the surface of a magnetic thin film, where the magnetic patterns are formed by milling $n\times n$ square holes on the surface of the film. The method is proposed for trapping and confining quantum degenerate gases, such as Bose-Einstein condensates and ultracold Fermi gases, prepared in low-magnetic-field-seeking states. Analytical expressions and numerical simulation results of the magnetic local minima are shown where we analyze the effect of changing the magnetic lattice parameters, such as the separation of the holes, the hole size, and external bias magnetic fields, to maintain and locate the nonzero local minima at a suitable distance above the film surface to avoid the effect of Majorana spin flips and the Casimir-Polder potential.

We propose a method to generate an isolated attosecond (as) pulse in combination with a chirped fundamental laser field ($5$ fs, $800$ nm) and a subharmonic laser field ($12$ fs, $1600$ nm). It is shown that, for the case of the chirped parameter $\beta =0.25$, not only is the efficiency of the extended harmonics enhanced, but also an ultrabroad supercontinuum is formed in the second plateau. For the case of $\beta =0.65$, an ultrabroad supercontinuum spectrum with the width of about $1670$ eV can be observed. Furthermore, due to the introduction of chirped pulse, the short quantum trajectory is enhanced, and the long one is suppressed. By superposing a properly selected range of the harmonic spectrum in the continuum region, an intense isolated 38-as pulse is generated.

We have measured the two-site double ionization of argon dimers by ultrashort laser pulses leading to fragmentation into two singly charged argon ions. Contrary to the expectations from a pure Coulomb explosion following rapid removal of one electron from each of the atoms, we find three distinct peaks in the kinetic energy release (KER) distribution. By measuring the angular distribution of the fragment ions and the vector momentum of one of the emitted electrons for circular and linear laser polarization, we are able to unravel the ionization mechanisms leading to the three features in the KER. The most abundant one results from tunnel ionization at one site followed by charge-enhanced tunnel ionization of the second atom. The second mechanism, which leads to a higher KER we identify as sequential tunnel ionization of both atoms accompanied by excitation. The third mechanism is present with linearly polarized light only. It is most likely a frustrated triple ionization, where the third electron does not escape but is trapped in a Rydberg state.

We investigate double ionization of argon dimers in high-intensity ultrashort Ti:sapphire laser pulses. We are able to identify several strong-field excitation pathways of the dimer that terminate in atomic ion pairs from a Coulomb explosion. The explosion starts from two-site double-ionized dimers and from one-site double-ionized ones after radiative charge transfer at small internuclear separation. One-site double ionization is accomplished by laser-induced charge transfer in the high-intensity laser pulse following two-site double ionization. The highest energy ion pairs we observed can be attributed to “frustrated triple ionization” of the argon dimer.

Many-electron systems confined to a quasi-one-dimensional geometry by a cylindrical distribution of positive charge have been investigated by density functional computations in the unrestricted local spin density approximation. Our investigations have been focused on the low-density regime, in which electrons are localized. The results reveal a wide variety of different charge and spin configurations, including linear and zig-zag chains, single- and double-strand helices, and twisted chains of dimers. The spin-spin coupling turns from weakly antiferromagnetic at relatively high density, to weakly ferromagnetic at the lowest densities considered in our computations. The stability of linear chains of localized charge has been investigated by analyzing the radial dependence of the self-consistent potential and by computing the dispersion relation of low-energy harmonic excitations.

We develop an accurate theory of resonantly interacting Fermi mixtures with both spin and mass imbalance. We consider Fermi mixtures with arbitrary mass imbalances but focus, in particular, on the experimentally available ${}^6\mathrm{Li}$-${}^{40}\mathrm{K}$ mixture. We determine the phase diagram of the mixture for different interactions strengths that lie on the BCS side of the Feshbach resonance. We also determine the universal phase diagram at unitarity. We find, for the mixtures with a sufficiently large mass imbalance, which includes the ${}^6\mathrm{Li}$-${}^{40}\mathrm{K}$ mixture, a Lifshitz point in the universal phase diagram that signals an instability toward a supersolid phase.

We study particle number fluctuations in the quantum ground states of a mixture of two spin-1 atomic condensates when the interspecies spin-exchange coupling interaction $c_{12}\beta$ is adjusted. The two spin-1 condensates forming the mixture are, respectively, ferromagnetic and polar in the absence of an external magnetic (B) field. We categorize all possible ground states using the angular momentum algebra and compute their characteristic atom number fluctuations, focusing especially on the the AA phase (when $c_{12}\beta >0$), where the ground state becomes fragmented and atomic-number fluctuations exhibit drastically different features from a single standalone spin-1 polar condensate. Our results are further supported by numerical simulations of the full quantum many-body system.