We present a new theoretical method to study a trapped gas of bosonic two-level atoms interacting with a single mode of a microwave cavity. This interaction is described by a trilinear Hamiltonian which is formally completely equivalent to the one describing parametric down-conversion in quantum optics. A system of differential equations describing the evolution, including the long-time behaviour, of not only the mean value but also the variance of the number of excited atoms is derived and solved analytically. For different initial states the mean number of excited atoms exhibits periodically reappearing dips, with an accompanying peak in the variance, or fractional collapses and revivals. Closed expressions for the period and the revival time are obtained.
We present a study of collapse-revival patterns that appear in the changes of atomic populations induced by the interaction of ultracold two-level atoms with electromagnetic cavities in resonance with an $m$-photon transition of the atoms ($m$-photon mazer). In particular, sech$^2$ and gaussian cavity mode profiles are considered and differences in the collapse-revival patterns are reported. The quantum theory of the $m$-photon mazer is written in the framework of the dressed-state coordinate formalism. Simple expressions for the atomic populations, the cavity photon statistics, and the reflec…
We study the dynamics of ultracold attractive atoms in a weakly linked two potential wells. We consider an unbalanced initial state and monitor dynamics of the population difference between the two wells. The average imbalance between wells undergoes damped oscillations, like in a classical counterpart, but then it revives almost to the initial value. We explain in details the whole behavior using three different models of the system. Furthermore we investigate the sensitivity of the revivals on the decoherence caused by one- and three-body losses. We include the dissipative processes using ap…
We propose a process to convert ultracold metastable Cs$_2$ molecules in their lowest triplet state into (singlet) ground state molecules in their lowest vibrational levels. Molecules are first pumped into an excited triplet state, and the triplet-singlet conversion is facilitated by a two-step spontaneous decay through the coupled $A^{1}Σ_{u}^{+} \sim b ^{3}Π_{u}$ states. Using spectroscopic data and accurate quantum chemistry calculations for Cs$_2$ potential curves and transition dipole moments, we show that this process has a high rate and competes favorably with the single-photon decay ba…
We present a proposal for controlling the conversion of ultracold atoms into molecules by fixing the phase difference between two oscillating magnetic fields. The scheme is based on the use of a magnetic Feshbach resonance with a field modulation that incorporates terms oscillating with frequencies corresponding to the main resonance and one of the subharmonics. The interference between the two association processes activated by the oscillating terms is controlled via the phase difference. As a result, significant increase or decrease of the effective interaction strength can be achieved. The …
We study the out-of-equilibrium dynamics of ultracold bosons in a double- and triple-well potential within the Bose-Hubbard model by means of the semiclassical Herman-Kluk propagator and compare the results to the frequently applied "classical dynamics" calculation in terms of the truncated Wigner approximation (TWA). For the double-well system we find the semiclassical results in excellent agreement with the numerically exact ones, while the TWA is not able to reproduce any revivals of the wave function. The triple-well system turns out to be more difficult to handle due to the irregularity o…
We study ground-state properties and dynamics of a dilute ultracold atomic gas in a double well potential. The Gaussian barrier separating the two wells derives from the interaction between the atoms and a quantized field of a driven Fabry-Perot cavity. Due to intrinsic atom-field nonlinearity, several novel phenomena arise being the focus of this work. For the ground state, there is a critical pumping amplitude in which the atoms self-organize and the intra cavity field amplitude drastically increases. In the dynamical analysis, we show that the Josephson oscillations depend strongly on the a…
High-efficiency photon-pair production is a long-sought-after goal for many optical quantum technologies, and coherent photon conversion processes are promising candidates for achieving this. We show theoretically how to control coherent conversion between a narrow-band pump photon and broadband photon pairs in nonlinear optical waveguides by tailoring frequency dispersion for broadband quantum frequency mixing. We reveal that complete deterministic conversion as well as pump-photon revival can be achieved at a finite propagation distance. We also find that high conversion efficiencies can be …
We explore the quantum dynamics of a one-dimensional trapped ultracold ensemble of bosonic atoms triggered by the sudden creation of a single ion. The numerical simulations are performed by means of the ab initio multiconfiguration time-dependent Hartree method for bosons which takes into account all correlations. The dynamics is analyzed via a cluster expansion approach, adapted to bosonic systems of fixed particle number, which provides a comprehensive understanding of the occurring many-body processes. After a transient during which the atomic ensemble separates into fractions which are unb…
The presence of quantum scars, athermal eigenstates of a many-body Hamiltonian with finite energy density, leads to absence of ergodicity and long-time coherent dynamics in closed quantum systems starting from simple initial states. Such non-ergodic coherent dynamics, where the system does not explore its entire phase space, has been experimentally observed in a chain of ultracold Rydberg atoms. We show, via study of a periodically driven Rydberg chain, that the drive frequency acts as a tuning parameter for several reentrant transitions between ergodic and non-ergodic regimes. The former regi…
The practical implementation of free-space quantum information tasks requires entanglement to be sustained over long distances and in the presence of turbulent and noisy environments. The transverse position-momentum entanglement of photon pairs produced by parametric down-conversion has found several uses in quantum information science, however, it is not suitable for applications involving long-distance propagation as the entanglement decays very rapidly when photons propagate away from their source. Entanglement is lost after a few centimetres of propagation, and the effect becomes even mor…
Robust stimulated Raman exact passages are requisite for controlling nonlinear quantum systems, with the wide applications ranging from ultracold molecules, non-linear optics to superchemistry. Inspired by shortcuts to adiabaticity, we propose the fast-forward scaling of stimulated Raman adiabatic processes with the nonlinearity involved, describing the transfer from an atomic Bose-Einstein condensate to a molecular one by controllable external fields. The fidelity and robustness of atom-molecule conversion are shown to surpass those of conventional adiabatic passages, assisted by fast-forward…
We report on two-photon photoassociation (PA) spectroscopy of ultracold heteronuclear LiRb molecules. This is used to determine the binding energies of the loosely bound levels of the electronic ground singlet and the lowest triplet states of LiRb. We observe strong two-photon PA lines with power broadened line widths greater than 20 GHz at relatively low laser intensity of 30 W/cm$^{2}$. The implication of this observation on direct atom to molecule conversion using stimulated Raman adiabatic passage (STIRAP) is discussed and the prospect for electronic ground state molecule production is the…
We propose a stroboscopic method to dynamically decouple the effects of two-body atom-atom interactions for ultracold atoms, and realize a system dominated by elastic three-body interactions. Using this method, we show that it is possible to achieve the optimal scaling behavior predicted for interaction-based quantum metrology with three-body interactions. Specifically, we show that for ultracold atoms quenched in an optical lattice, we can measure the three-body interaction strength with a precision proportional to ${\bar n}^{-5/2}$ using homodyne quadrature interferometry, and ${\bar n}^{-7/…
We show that the effect of measurement back-action results in the generation of multiple many-body spatial modes of ultracold atoms trapped in an optical lattice, when scattered light is detected. The multipartite mode entanglement properties and their nontrivial spatial overlap can be varied by tuning the optical geometry in a single setup. This can be used to engineer quantum states and dynamics of matter fields. We provide examples of multimode generalizations of parametric down-conversion, Dicke, and other states, investigate the entanglement properties of such states, and show how they ca…
Majorana physics in a Luttinger liquid with attractive interactions
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Max-Planck-Institute for Quantum Optics（马克斯·普朗克量子光学研究所）；Politecnico di Torino（都灵理工大学）
The conversion of ultracold atoms to molecules via a magnetic Feshbach resonance with a sinusoidal modulation of the field is studied. Different practical realizations of this method in Bose atomic gases are analyzed. Our model incorporates many-body effects through an effective reduction of the complete microscopic dynamics. Moreover, we simulate the experimental conditions corresponding to the preparation of the system as a thermal gas and as a condensate. Some of the experimental findings are clarified. The origin of the observed dependence of the production efficiency on the frequency, amp…
We investigate magnetoassociation of ultracold fermionic Feshbach molecules in a mixture of $^{40}$K and $^{87}$Rb atoms, where we can create as many as $7\times 10^4$ $^{40}$K$^{87}$Rb molecules with a conversion efficiency as high as 45%. In the perturbative regime, we find that the conversion efficiency depends linearly on the density overlap of the two gases, with a slope that matches a parameter-free model that uses only the atom masses and the known Feshbach resonance parameters. In the saturated regime, we find that the maximum number of Feshbach molecules depends on the atoms' phase-sp…
Hybrid quantum systems involving cold atoms and microwave resonators can enable cavity-mediated infinite-range interactions between atomic spin systems and realize atomic quantum memories and transducers for microwave to optical conversion. To achieve strong coupling of atoms to on-chip microwave resonators, it was suggested to use atomic Rydberg states with strong electric dipole transitions. Here we report on the realization of coherent coupling of a Rydberg transition of ultracold atoms trapped on an integrated superconducting atom chip to the microwave field of an on-chip coplanar waveguid…
