A method is proposed to cool down atoms in a harmonic trap without phase-space compression as in a perfectly slow adiabatic expansion, i.e., keeping the populations of the instantaneous initial and final levels invariant, but in a much shorter time. This may require that the harmonic trap becomes an expulsive parabolic potential in some time interval. The cooling times achieved are also shorter than previous minimal times using optimal-control bang-bang methods and real frequencies.PACS numbers: 37.10. De, 37.10.Vz A fast adiabatic expansion in a short finite time looks like a contradiction in terms. An "adiabatic" process in quantum mechanics is a slow process where the system follows at all times the instantaneous eigenvalues and eigenstates of the time-dependent Hamiltonian. This is in a sense maximally efficient as the populations do not change, i.e. there is no heating or friction, but the price to pay is that the long times needed may render the process useless or even impossible to implement. Thus, a highly desirable goal is to prepare the same final states and energies of the adiabatic process in a given finite time t f , without necessarily following the instantaneous eigenstates along the way. We would also like the process to be robust with respect to arbitrary initial states. If fulfilled, this old goal [1] has important implications. In particular, cooling without phase-space compression, which is all that is needed for many applications other than Bose Einstein condensation, could be performed in fast cycles increasing, for example, the flux of cold atoms produced and the signal to noise ratio in an atomic clock [2], or in cold-atom pulsed beam experiments and related technology [3]. This goal also includes as a particular case a long standing question in the fields of optimal control theory and finite time thermodynamics, namely, to optimize the passage between two thermal states of a system [4,5,6,7]. For time-dependent harmonic oscillators, minimal times have been established using "bang-bang" real-frequency processes believed up to now to be optimal [6], in which the frequencies are changed suddenly at certain instants but kept constant otherwise. In this letter we shall describe a robust solution to the stated general goal for atoms trapped in a time-dependent harmonic oscillator which applies both to equilibrium and non-equilibrium states. In particular we describe cooling processes performed in a time interval smaller than the minimal time of the bang-bang methods considered so far. We shall for simplicity describe our method for states representing single atoms of mass m, but the same results are immediately applicable to N -body non-interacting fermions or to a Tonks-Girardeau gas [8], and generalizations will be relevant for other driving processes, such as cold atom launching or the transport of ultracold atoms with optical tweezers [9].We consider an effectively one dimensional time dependent harmonic oscillator, H =p 2 /2m + mω(t) 2q2 /2, with an initial angular frequency ω(0) > 0 a...

The Jaynes-Cummings model describes the coupling between photons and a single two-level atom in a simplified representation of light-matter interactions. In circuit QED, this model is implemented by combining microwave resonators and superconducting qubits on a microchip with unprecedented experimental control. Arranging qubits and resonators in the form of a lattice realizes a new kind of Hubbard model, the Jaynes-Cummings-Hubbard model, in which the elementary excitations are polariton quasiparticles. Due to the genuine openness of photonic systems, circuit QED lattices offer the possibility to study the intricate interplay of collective behavior, strong correlations and non-equilibrium physics. Thus, turning circuit QED into an architecture for quantum simulation, i.e., using a wellcontrolled system to mimic the intricate quantum behavior of another system too daunting for a theorist to tackle head-on, is an exciting idea which has served as theorists' playground for a while and is now also starting to catch on in experiments. This review gives a summary of the most recent theoretical proposals and experimental efforts.

We report on the engineering of a non-dispersive (flat) energy band in a geometrically frustrated lattice of micro-pillar optical cavities. By taking advantage of the non-hermitian nature of our system, we achieve bosonic condensation of exciton-polaritons into the flat band. Due to the infinite effective mass in such band, the condensate is highly sensitive to disorder and fragments into localized modes reflecting the elementary eigenstates produced by geometric frustration. This realization offers a novel approach to studying coherent phases of light and matter under the controlled interplay of frustration, interactions and dissipation.

Mediated photon-photon interactions are realized in a superconducting coplanar waveguide cavity coupled to a superconducting charge qubit. These nonresonant interactions blockade the transmission of photons through the cavity. This so-called dispersive photon blockade is characterized by measuring the total transmitted power while varying the energy spectrum of the photons incident on the cavity. A staircase with four distinct steps is observed and can be understood in an analogy with electron transport and the Coulomb blockade in quantum dots. This work differs from previous efforts in that the cavity-qubit excitations retain a photonic nature rather than a hybridization of qubit and photon and provides the needed tolerance to disorder for future condensed matter experiments.

We report here the experimental observation of a dynamical quantum phase transition in a strongly interacting open photonic system. The system studied, comprising a Jaynes-Cummings dimer realized on a superconducting circuit platform, exhibits a dissipation driven localization transition. Signatures of the transition in the homodyne signal and photon number reveal this transition to be from a regime of classical oscillations into a macroscopically self-trapped state manifesting revivals, a fundamentally quantum phenomenon. This experiment also demonstrates a small-scale realization of a new class of quantum simulator, whose well controlled coherent and dissipative dynamics is suited to the study of quantum many-body phenomena out of equilibrium.Comment: 34 pages, 13 figures, includes supplementary material; significant additions to theory section

We demonstrate a coupled cavity realization of a Bose Hubbard dimer to achieve quantum limited amplification and to generate frequency entangled microwave fields with squeezing parameters well below -12 dB. In contrast to previous implementations of parametric amplifiers our dimer can be operated both as a degenerate and as a nondegenerate amplifier. The large measured gain-bandwidth product of more than 250 MHz for nondegenerate operation and the saturation at input photon numbers as high as 2000 per µs are both expected to be improvable even further, while maintaining wide frequency tunability of about 2 GHz. Featuring flexible control over all relevant system parameters, the presented Bose-Hubbard dimer based on lumped element circuits has significant potential as an elementary cell in nonlinear cavity arrays for quantum simulation.The high level of control achievable over collections of massive or massless particles, such as atoms, spins or photons, enables the detailed study of intricate many-body phenomena in man-made quantum systems [1]. In this context coupled nonlinear resonators both provide a viable avenue for studying light-matter interactions and constitute a generic building block for photonic quantum simulators of strongly interacting systems [2][3][4]. Therefore, their theoretical and experimental investigation is pursued in a wide variety of physical settings such as photonic structures [5,6], optomechanical systems [7][8][9] and superconducting circuits [10][11][12].The remarkable progress in quantum science using microwave radiation has stimulated broad interest in low noise amplification [13,14] and has lead to the development of novel versatile amplifiers in the recent years [15][16][17][18][19][20][21][22]. Many of these implementations rely on parametric processes in which the noise temperature of the amplifier is solely limited by the radiation temperature of the input fields, ultimately by the vacuum fluctuations [23]. In parametric amplification the presence of a signal stimulates conversion processes from a pump field into the signal field, while creating an additional idler field. When signal and idler field occupy the same mode, this is referred to as degenerate parametric amplification, whereas in nondegenerate amplifiers the signal and idler modes are separated either spatially or in frequency [23]. While degenerate parametric amplifiers [15] are often preferable for the fast dispersive readout of qubits in quantum feedback protocols, nondegenerate amplification [19] can be more practical for multiplexed readout, the measurement of photon correlation functions and more general applications in which amplification is to be independent of the phase of the signal relative to the pump.Here, we consider a system described by two bosonic modes a L and a R , which are coupled with hopping rate J and have an on-site interaction strength U = U L = U R , see generic representation in Fig. 1(a). In a frame rotating at the bare cavity frequency ω 0 = ω L = ω R the system is described by the Bos...

We show that photons in two tunnel-coupled microwave resonators each containing a single superconducting qubit undergo a sharp non-equilibrium delocalization-localization (self-trapping) transition due to strong photon-qubit coupling. We find, that self-trapping of photons in one of the resonators (spatial localization) forces the qubit in the opposite resonator to remain in its initial state (energetic localization). This allows for an easy experimental observation of the transition by local read-out of the qubit state. Dissipation of photons and decoherence of the qubit favor the self-trapped regime.

We present an analytic strong-coupling approach to the phase diagram and elementary excitations of the Jaynes-Cummings-Hubbard model describing a superfluid-insulator transition of polaritons in an array of coupled QED cavities. In the Mott phase, we find four modes corresponding to particle/hole excitations with lower and upper polaritons, respectively. Simple formulas are derived for the dispersion and spectral weights within a strong-coupling random-phase approximation (RPA). The phase boundary is calculated beyond RPA by including the leading correction due to quantum fluctuations.The recent experimental success in engineering strong interactions between photons and atoms in high-quality micro-cavities opens up the possibility to use lightmatter systems as quantum simulators for many-body physics [1]. A prominent example is the superfluidinsulator transition of polaritons in an array of coupled QED cavities as described by the Jaynes-CummingsHubbard model (JCHM) [2,3]. The competition between strong atom-photon coupling, giving rise to an effective photon repulsion (localization), and the photon hopping between cavities (delocalization) leads to a quantum phase diagram featuring Mott lobes [2] reminiscent of those of ultracold atoms in optical lattices as described by the seminal Bose-Hubbard model (BHM) [4]. The JCHM can be implemented, e.g. using single atoms [5], excitons [6], or Cooper pairs [7]. The striking advantage of using coupled micro-cavities, with respect to their optical lattice counterparts, is their individual accessibility.Although the coupling between QED cavities has not yet been implemented experimentally, the JCHM stimulated exciting theoretical work over the last three years, suggesting that polariton systems can be used to simulate various strongly correlated and exotic phases [8,9,10,11,12,13]. While such exploratory work is justified in its own right, still very little is known about the fundamental excitations of the JCHM. The phase boundary of the superfluid-insulator transition has been calculated using mean-field decoupling [2,8], 15] and variational cluster approaches [16,17] in two and three dimensions. Only two papers have explored the fundamental excitations of the system [15,17]. All of these results, even on a mean-field level, rely on more or less heavy numerical computation due to the intricate composite nature of polaritons. To the best of our knowledge, no analytic results are available neither for the phase boundary nor for the excitations of the JCHM.In this paper, we show that a linked-cluster expansion pioneered for the Fermi-Hubbard model (FHM) [18] and recently applied to the BHM [19] can be used to obtain simple, analytic formulas for the phase diagram as well as excitation spectra for arbitrary temperatures, detuning parameter and lattice geometries. We find two new modes, which have been overlooked in previous numerical approaches and discuss dispersion and spectral weights within strong-coupling RPA. Furthermore, we study the effect of quantum fluctuations on ...