81 research outputs found
Quench dynamics of a disordered array of dissipative coupled cavities
We investigate the mean-field dynamics of a system of interacting photons in
an array of coupled cavities in presence of dissipation and disorder. We follow
the evolution of on an initially prepared Fock state, and show how the
interplay between dissipation and disorder affects the coherence properties of
the cavity emission and that these properties can be used as signatures of the
many-body phase of the whole array.Comment: 8 pages, 10 figures, new reference adde
Nonreciprocal signal routing in an active quantum network
As superconductor quantum technologies are moving towards large-scale integrated circuits, a robust and flexible approach to routing photons at the quantum level becomes a critical problem. Active circuits, which contain parametrically driven elements selectively embedded in the circuit, offer a viable solution. Here, we present a general strategy for routing nonreciprocally quantum signals between two sites of a given lattice of oscillators, implementable with existing superconducting circuit components. Our approach makes use of a dual lattice of overdamped oscillators linking the nodes of the main lattice. Solutions for spatially selective driving of the lattice elements can be found, which optimally balance coherent and dissipative hopping of microwave photons to nonreciprocally route signals between two given nodes. In certain lattices these optimal solutions are obtained at the exceptional point of the dynamical matrix of the network. We also demonstrate that signal and noise transmission characteristics can be separately optimized
Nonequilibrium gas-liquid transition in the driven-dissipative photonic lattice
We study the nonequilibrium steady state of the driven-dissipative
Bose-Hubbard model with Kerr nonlinearity. Employing a mean-field decoupling
for the intercavity hopping , we find that the steep crossover between low
and high photon-density states inherited from the single cavity transforms into
a gasliquid bistability at large cavity-coupling . We formulate a van der
Waals like gasliquid phenomenology for this nonequilibrium situation and
determine the relevant phase diagrams, including a new type of diagram where a
lobe-shaped boundary separates smooth crossovers from sharp, hysteretic
transitions. Calculating quantum trajectories for a one-dimensional system, we
provide insights into the microscopic origin of the bistability.Comment: 5 pages, 4 figures + Supplemental Material (2 pages, 2 figures
An efficient Fredholm method for calculation of highly excited states of billiards
A numerically efficient Fredholm formulation of the billiard problem is
presented. The standard solution in the framework of the boundary integral
method in terms of a search for roots of a secular determinant is reviewed
first. We next reformulate the singularity condition in terms of a flow in the
space of an auxiliary one-parameter family of eigenproblems and argue that the
eigenvalues and eigenfunctions are analytic functions within a certain domain.
Based on this analytic behavior we present a numerical algorithm to compute a
range of billiard eigenvalues and associated eigenvectors by only two
diagonalizations.Comment: 15 pages, 10 figures; included systematic study of accuracy with 2
new figures, movie to Fig. 4,
http://www.quantumchaos.de/Media/0703030media.av
Exotic attractors of the non-equilibrium Rabi-Hubbard model
We explore the phase diagram of the dissipative Rabi-Hubbard model, as could
be realized by a Raman-pumping scheme applied to a coupled cavity array. There
exist various exotic attractors, including ferroelectric, antiferroelectric,
and inccomensurate fixed points, as well as regions of persistent oscillations.
Many of these features can be understood analytically by truncating to the two
lowest lying states of the Rabi model on each site. We also show that these
features survive beyond mean-field, using Matrix Product Operator simulations.Comment: 5pages, 3 figures, plus supplementary material. Final version, as
publishe
Non-equilibrium delocalization-localization transition of photons in circuit QED
We show that photons in two tunnel-coupled microwave resonators each
containing a single superconduct- ing qubit undergo a sharp non-equilibrium
delocalization-localization (self-trapping) transition due to strong
photon-qubit coupling. We find that dissipation favors the self-trapped regime
and leads to the possibility of observing the transition as a function of time
without tuning any parameter of the system. Furthermore, 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.Comment: 4 pages, 5 figure
Theory of the spatial structure of non-linear lasing modes
A self-consistent integral equation is formulated and solved iteratively
which determines the steady-state lasing modes of open multi-mode lasers. These
modes are naturally decomposed in terms of frequency dependent biorthogonal
modes of a linear wave equation and not in terms of resonances of the cold
cavity. A one-dimensional cavity laser is analyzed and the lasing mode is found
to have non-trivial spatial structure even in the single-mode limit. In the
multi-mode regime spatial hole-burning and mode competition is treated exactly.
The formalism generalizes to complex, chaotic and random laser media.Comment: 4 pages, 3 figure
Pump-induced Exceptional Points in Lasers
We demonstrate that the above-threshold behavior of a laser can be strongly
affected by exceptional points which are induced by pumping the laser
nonuniformly. At these singularities, the eigenstates of the non-Hermitian
operator which describes the lasing modes coalesce. In their vicinity, the
laser may turn off even when the overall pump power deposited in the system is
increased. Such signatures of a pump- induced exceptional point can be
experimentally probed with coupled ridge or microdisk lasers.Comment: 4.5 pages, 4 figures, final version including additional FDTD dat
Photon correlations in a two-site non-linear cavity system under coherent drive and dissipation
We calculate the normalized second-order correlation function for a system of
two tunnel-coupled photonic resonators, each one exhibiting a single-photon
nonlinearity of the Kerr type. We employ a full quantum formulation: the master
equation for the model, which takes into account both a coherent continuous
drive and radiative as well as non-radiative dissipation channels, is solved
analytically in steady state through a perturbative approach, and the results
are compared to exact numerical simulations. The degree of second-order
coherence displays values between 0 and 1, and divides the diagram identified
by the two energy scales of the system - the tunneling and the nonlinear Kerr
interaction - into two distinct regions separated by a crossover. When the
tunneling term dominates over the nonlinear one, the system state is
delocalized over both cavities and the emitted light is coherent. In the
opposite limit, photon blockade sets in and the system shows an insulator-like
state with photons locked on each cavity, identified by antibunching of emitted
light.Comment: 9 pages, 4 figures, to appear in Phys. Rev.
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