Michael J. Hartmann

Strongly Interacting Polaritons in Coupled Arrays of Cavities

Observing quantum phenomena in strongly correlated many-particle systems is difficult because of the short length- and timescales involved. Exerting control over the state of individual elements within such a system is even more so, and represents a hurdle in the realization of quantum computing devices. Substantial progress has been achieved with arrays of Josephson junctions and cold atoms in optical lattices, where detailed control over collective properties is feasible, but addressing individual sites remains a challenge. Here we show that a system of polaritons held in an array of resonant optical cavities—which could be realized using photonic crystals or toroidal microresonators—can form a strongly interacting many-body system showing quantum phase transitions, where individual particles can be controlled and measured. The system also offers the possibility to generate attractive on-site potentials yielding highly entangled states and a phase with particles much more delocalized than in superfluids.

Quantum many-body phenomena in coupled cavity arrays

The increasing level of experimental control over atomic and optical systems gained in the past years have paved the way for the exploration of new physical regimes in quantum optics and atomic physics, characterised by the appearance of quantum many-body phenomena, originally encountered only in condensed-matter physics, and the possibility of experimentally accessing them in a more controlled manner. In this review article we survey recent theoretical studies concerning the use of cavity quantum electrodynamics to create quantum many-body systems. Based on recent experimental progress in the fabrication of arrays of interacting micro-cavities and on their coupling to atomic-like structures in several different physical architectures, we review proposals on the realisation of paradigmatic many-body models in such systems, such as the Bose-Hubbard and the anisotropic Heisenberg models. Such arrays of coupled cavities offer interesting properties as simulators of quantum many-body physics, including the full addressability of individual sites and the accessibility of inhomogeneous models.

Photon blockade in the ultrastrong coupling regime.

We explore photon coincidence counting statistics in the ultrastrong coupling regime, where the atom-cavity coupling rate becomes comparable to the cavity resonance frequency. In this regime, usual normal order correlation functions fail to describe the output photon statistics. By expressing the electric-field operator in the cavity-emitter dressed basis, we are able to propose correlation functions that are valid for arbitrary degrees of light-matter interaction. Our results show that the standard photon blockade scenario is significantly modified for ultrastrong coupling. We observe parametric processes even for two-level emitters and temporal oscillations of intensity correlation functions at a frequency given by the ultrastrong photon emitter coupling. These effects can be traced back to the presence of two-photon cascade decays induced by counterrotating interaction terms.

Strong photon nonlinearities and photonic mott insulators

We show that photon nonlinearities in an electromagnetically induced transparency can be at least 1 order of magnitude larger than predicted in all previous approaches. As an application we demonstrate that in this regime they give rise to very strong photon-photon interactions which are strong enough to make an experimental realization of a photonic Mott insulator state feasible in arrays of coupled ultrahigh-Q microcavities.

Polariton crystallization in driven arrays of lossy nonlinear resonators.

We investigate the steady states of a lossy array of nonlinear optical resonators that are driven by lasers and interact via mutual photon tunneling. For weak nonlinearities, we find two-mode squeezing of polaritons in modes whose quasimomenta match the relative phases of the laser drives. For strong nonlinearities the spatial polariton density-density correlations indicate that the polaritons crystallize and are predominantly found at a specific distance from each other despite being injected by a coherent light source and damped by the environment.

Photon solid phases in driven arrays of nonlinearly coupled cavities.

We introduce and study the properties of an array of QED cavities coupled by nonlinear elements, in the presence of photon leakage and driven by a coherent source. The nonlinear couplings lead to photon hopping and to nearest-neighbor Kerr terms. By tuning the system parameters, the steady state of the array can exhibit a photon crystal associated with a periodic modulation of the photon blockade. In some cases, the crystalline ordering may coexist with phase synchronization. The class of cavity arrays we consider can be built with superconducting circuits of existing technology.

Existence of Temperature on the Nanoscale

We consider a regular chain of quantum particles with nearest neighbor interactions in a canonical state with temperature T. We analyze the conditions under which the state factors into a product of canonical density matrices with respect to groups of n particles each and under which these groups have the same temperature T. In quantum mechanics the minimum group size n(min) depends on the temperature T, contrary to the classical case. We apply our analysis to a harmonic chain and find that n(min)=const for temperatures above the Debye temperature and n(min) proportional to T(-3) below.

Quantum information processing with nanomechanical qubits.

We introduce an approach to quantum information processing where the information is stored in the motional degrees of freedom of nanomechanical devices. The qubits of our approach are formed by the two lowest energy levels of mechanical resonators, which are tuned to be strongly anharmonic by suitable electrostatic fields. Single qubit rotations are conducted by radio-frequency voltage pulses that are applied to individual resonators. Two-qubit entangling gates in turn are implemented via a coupling of two qubits to a common optical resonance of a high finesse cavity. We find that gate fidelities exceeding 99% can be achieved for realistic experimental parameters.

Bose–Hubbard dynamics of polaritons in a chain of circuit quantum electrodynamics cavities

We investigate a chain of superconducting stripline resonators, each interacting with a transmon qubit, that are capacitively coupled in a row. We show that the dynamics of this system can be described by a Bose–Hubbard Hamiltonian with attractive interactions for polaritons, superpositions of photons and qubit excitations. This setup, we envisage, is one of the first platforms where all the technological components that are needed to experimentally study chains of strongly interacting polaritons have already been realized. By driving the first stripline resonator with a microwave source and detecting the output field of the last stripline resonator, one can spectroscopically probe the properties of the system in the driven dissipative regime. We calculate the stationary polariton density and density–density correlations g(2) for the last cavity, which can be measured via the output field. Our results display a transition from a coherent to a quantum field as the ratio of on-site interactions to driving strength is increased.

Spontaneous conversion from virtual to real photons in the ultrastrong-coupling regime.

We show that a spontaneous release of virtual photon pairs can occur in a quantum optical system in the ultrastrong coupling regime. In this regime, which is attracting interest both in semiconductor and superconducting systems, the light-matter coupling rate Ω(R) becomes comparable to the bare resonance frequency of photons ω(0). In contrast to the dynamical Casimir effect and other pair creation mechanisms, this phenomenon does not require external forces or time dependent parameters in the Hamiltonian.