Session B29: Focus Session: Quantum Optics with Superconducting Circuits: Many-Body Physics, Phase Transitions, & Bistability

Cavity-Free Photon Blockade Induced by Many-Body Bound States

We show theoretically that a variety of strong quantum nonlinear phenomena occur in a completely open one-dimensional waveguide coupled to an N-type four-level system. This system could be realized, for example, in experiments using superconducting circuits. We focus on photon blockade, photon-induced tunneling, bunching or anti-bunching, and the creation of single-photon states, all in the absence of a cavity. Many-body bound states appear due to the strong photon-photon correlation mediated by the four-level system. These bound states cause photon blockade, generating a sub-Poissonian single-photon source [1]. Such a source is crucial for quantum cryptography and distributed quantum networking; our work thus supports the notion that open quantum systems can play a critical role in the manipulation of individual, mobile quanta, a key goal of quantum communication. [1] H. Zheng, D. J. Gauthier, and H. U. Baranger, Phys. Rev. Lett. in press (2011), arXiv:1107.0309.   

Experimental investigation of a nonequilibrium delocalization-localization transition of photons in circuit quantum electrodynamics

Strong photon-qubit coupling in the circuit quantum electrodynamics architecture may lead to quantum phase transitions of light. Recent theoretical and experimental efforts have been made toward examining such quantum phase transitions in large systems; however, interesting crossovers may also exist in significantly smaller and more controllable systems. A sharp nonequilibrium self-trapping transition of light has been predicted in a system comprising two coupled resonators each containing a single qubit. A delocalized regime, where photons coherently oscillate between the two cavities, transitions via dissipation into a localized regime, where photons cannot tunnel. We realized this system experimentally using two capacitively coupled superconducting microwave coplanar waveguides each containing a single transmon qubit. We present our experimental investigation of the system using time and frequency domain measurements to probe its dynamics.   

Disorder in a Kagome Lattice of Superconducting Coplanar Waveguide Resonators

It has been proposed that arrays of electromagnetic cavities, coupled to two level quantum systems can be used to realize quantum phase transitions of polaritons. One possible experimental realization is a circuit quantum electrodynamics architecture, in which transmon qubits are coupled to superconducting coplanar waveguide resonators (CPWRs); however, for this to be successful, arrays of resonators must be fabricated with low disorder. Results will be reported on characterization of an array of 12 niobium resonators on a sapphire substrate in a honeycomb pattern with the photonic lattice sites forming a Kagome star. These arrays were characterized by measuring many devices of the same design, and using statistical methods for analysis. Furthermore we investigate the origins of disorder, and its dependence on fluctuations in the CPWR geometry.   

Double symmetry breaking and 2D quantum phase diagram in spin-boson systems

When the collective coupling between a chain of spins (two-levels systems) and a bosonic mode becomes comparable with the two-level transition frequency, superradiant quantum phase transitions for the cavity vacuum can occur, for instance within the Dicke model [1]. Here, the quantum ground state properties of two independent chains of pseudo-spins interacting with the same bosonic field are investigated [2] . Each chain is coupled to a different quadrature of the field, leading to two independent symmetry breakings for increasing values of the two spin-boson interaction constants. A 2D phase diagram is provided with 4 different phases that can be characterized by the complex bosonic coherence of the ground states and can be manipulated via non-abelian Berry effects. Possible realizations of such model in circuit QED are discussed, generalizing the previous proposals to implement the standard Dicke model [3,4]. \\[4pt] [1] C. Emary, and T. Brandes, Phys. Rev. Lett. 90, 044101 (2003).\\[0pt] [2] P. Nataf, A. Baksic and C. Ciuti, arXiv:1111.1617 (2011).\\[0pt] [3] P. Nataf and C. Ciuti, Nat. Commun. 1 :72 (2010).\\[0pt] [4] P. Nataf and C. Ciuti, Phys. Rev. Lett. 104, 023601 (2010).   

Quantum hysteresis in coupled qubit-radiation systems

We study theoretically the dynamical response of a set of solid-state qubits arbitrarily coupled to a radiation field which is confined in a cavity. Driving the coupling strength in round trips, between weak and strong values, we quantify the hysteresis or irreversible quantum dynamics. The matter-radiation system is modeled as a finite-size Dicke model which has previously been used to describe equilibrium (including quantum phase transition) properties of systems such as quantum dots in a microcavity, and superconducting circuit QED. Here we extend this model to address {\it non-equilibrium} situations. Analyzing the system's quantum fidelity, we find that the near-adiabatic regime exhibits the richest phenomena, with a strong asymmetry in the internal collective dynamics depending on which phase is chosen as the starting point. We identify significant deviations from the conventional Landau-Zener-Stuckelberg formulae, in particular from cycles starting in the superradiant phase. In the diabatic or impulsive regime, the system remains quenched and there is little hysteresis. By contrast, depending on the specifications of the cycle, the radiation subsystem can exhibit the emergence of non-classicality, complexity and sub-Planckian structures as evidenced by its Wigner function.   

Coupled Qubit-Cavity Arrays: Evolution of resonance with hopping

Recent experiments on the light-matter interaction in superconducting qubits have sparked interest in the prospect of studying collective behaviour of coupled qubit-cavity arrays. Any such behaviour will necessarily be non-equilibrium, as the photon loss present in real cavities must be compensated by pumping. We study an array of coupled qubit-cavity systems, with the simplest pumping scheme, using a coherent field. Such pumping might be thought to destroy any interesting physics by imposing coherence on the system. Yet we show that the emerging phenomena are remarkably rich, focussing on the evolution from the antiresonance feature known in the Jaynes-Cummings model [1] as one increases hopping strength between the coupled cavities. We study both the coherent field (as can be measured by homodyne detection) and the fluorescence spectrum, comparing numerical simulations to analytic approximations valid in the limits of large and small hopping. The steady state coherent field depends non-monotonically on the hopping strength, as a crossover occurs from polariton blockade physics at small hopping to semiclassical behaviour at large hopping. \\[4pt] [1] Bishop et al., Nat. Phys. 5, 105 - 109 (2009)   

Superradiant Phase Transitions and the Standard Description of Circuit QED

We investigate the equilibrium behavior of a superconducting circuit QED system containing a large number of artificial atoms. It is shown that the currently accepted standard description of circuit QED via an effective model fails in an important aspect: it predicts the possibility of a superradiant phase transition, even though a full microscopic treatment reveals that a no-go theorem for such phase transitions known from cavity QED applies to circuit QED systems as well. We generalize the no-go theorem to the case of (artificial) atoms with many energy levels and thus make it more applicable for realistic cavity or circuit QED systems.   

Photon thermalization and condensation in circuit QED by engineered dissipation

The ability to engineer the coupling between a quantum system and its environment opens the possibility to dissipatively prepare entangled and quantum many- body states. Of particular interest is the case in which the system undergoes a phase transition driven by the coupling to a reservoir. Here we show how to engineer dissipation in the context of coupled cavity arrays, and more specifically in circuit QED. We propose an implementation based on coupled LC resonators and superconducting qubits, which under asymmetric coherent driving, leads to thermalization of photons to the symmetric state between neighboring sites. Above a critical threshold of the driving intensity, a macroscopic occupation of this symmetric mode is found.   

Stabilizing manifolds of quantum states by reservoir engineering

We consider the problem of stabilizing a manifold of states by reservoir engineering. Qubits are coupled to resonators in the strong dispersive limit for which the dispersive shift is much larger than the cavity decay rate. The resonators are driven by microwave fields. By adequately choosing the frequencies of these fields, we can transfer the entropy of the quantum system into its environment. This stabilization is autonomous and continuous in time, and does not rely on a precise control of the drive field amplitudes. The scheme does not require any knowledge of measurement outcomes thus simplifying its experimental realization. Experimental data on dynamical cooling of a transmon qubit coupled to a compact resonator will be shown. Finally, applications to quantum error correction will be discussed.   

Adiabatic state preparation of interacting two-level systems

We consider performing adiabatic rapid passage (ARP) using frequency-swept optical pulses to excite a collection of interacting two-level systems. Such a model arises in a wide range of many body quantum systems, such as circuit QED or interacting quantum dots, where a nonlinear component couples to light. We analyse the one-dimension case using the Jordan-Wigner transformation. In the mean field limit, the system can be described by a Lipkin-Meshkov-Glick Hamiltonian. Both approaches provide complementary insights into the behaviour of an interacting model under ARP, suggesting our results are generically applicable. We find ARP can still be used for state preparation in the presence of interactions but the parameters required to achieve full occupation depend on the strength of the interaction. In particular, for a fixed pulse time, stronger interactions require a larger pulse bandwidth, introducing new restrictions on the pulse form required.   

Collective quantum coherence in large superconducting circuits with approximate $S_N$ symmetry

The vast majority of superconducting circuits consist of a minimum number of circuit elements, following an implicit conjecture that any increase in circuit complexity thwarts quantum coherence. Recent experiments have evidenced that this conjecture is not compelling and quantum coherence can persist for much larger circuits~[1]. A tool for the design of future circuits, we present theory for the fluxonium qubit, a device which includes a large number, $N$, of array junctions. Taking into account the degrees of freedom of all junctions and the approximate $S_N$ permutation symmetry, we identify the relevant collective mode and pinpoint an approximate decoupling of additional modes. This allows us to derive the effective models previously used. We also discuss corrections going beyond these models which include subspaces of states that transform as non-trivial representations of the permutation group. \par\noindent [1]~V.\ E.\ Manucharyan, J.\ Koch, L.\ I.\ Glazman, and M.\ H.\ Devoret, Science {\bf 326\/}, 113 (2009)   

Quantum crossover of the switching rate of a modulated oscillator

Experiments with Josephson bifurcation amplifiers have reached the regime where switching between coexisting stable vibrational states is due to quantum fluctuations. In switching the oscillator goes over the effective dynamical barrier that separates the states. It was found earlier that, for small damping, the barrier height calculated for $T\to 0$ is smaller than for $T=0$. Respectively, the switching rates calculated in these two limits are exponentially different, the effect of fragility. If other parameters are fixed, both barrier heights are proportional to the number of bound quantum states localized mostly in the basin of attraction of the corresponding stable state. Here we show that for large but finite values of the number of states the $T=0$ solution is stabilized. For some temperature $T_c$ there occurs a sharp crossover to the finite-temperature regime. Our analytical results are corroborated by numerical results.\\[4pt] [1] Vijay et al., Rev. Sci. Instr. (2009)\\[0pt] [2] M. Dykman et al., JETP (1988)\\[0pt] [3] M. Marthaler et al, PRA (2005)   

Observation of single artificial atom optical bi-stability and its application to single-shot readout in circuit quantum electrodynamics

The high power transient behavior of superconducting qubit-cavity systems has recently been used to perform high fidelity readout of transmon qubits [1]. We show that in the steady state, the system exhibits a bi-stable behavior that can be observed on the single-shot level, with the cavity state switching stochastically between dim and bright states. The switching times are shown to be long compared to the cavity and qubit lifetimes. Some features of the bi-stability can be explained by mean field theory, while its switching dynamics is studied with large scale simulations. Understanding these dynamics will be crucial for studying the transient response, an essential aspect of the qubit readout. We will discuss progress on optimizing readout by shaping the measurement pulse. \\[4pt] [1] M. D. Reed, L. DiCarlo, B. R. Johnson, L. Sun, D. I. Schuster, L. Frunzio, and R. J. Schoelkopf, Phys. Rev. Lett. 105, 173601 (2010)