Exotic interactions mediated by a non-Hermitian photonic bath

Nature communications, 2018

Zero-energy particles (such as Majorana fermions) are newly predicted quasiparticles and are expected to play an important role in fault-tolerant quantum computation. In conventional Hermitian quantum systems, however, such zero states are vulnerable and even become vanishing if couplings with surroundings are of the same topological nature. Here we demonstrate a robust photonic zero mode sustained by a spatial non-Hermitian phase transition in a parity-time (PT) symmetric lattice, despite the same topological order across the entire system. The non-Hermitian-enhanced topological protection ensures the reemergence of the zero mode at the phase transition interface when the two semi-lattices under different PT phases are decoupled effectively in their real spectra. Residing at the midgap level of the PT symmetric spectrum, the zero mode is topologically protected against topological disorder. We experimentally validated the robustness of the zero-energy mode by ultrafast heterodyne m...

Scientific Reports, 2015

We propose an optical simulation of dissipation-induced correlations in one-dimensional (1D) interacting bosonic systems, using a two-dimensional (2D) array of linear photonic waveguides and only classical light. We show that for the case of two bosons in a 1D lattice, one can simulate on-site two-body dissipative dynamics using a linear 2D waveguide array with lossy diagonal waveguides. The intensity distribution of the propagating light directly maps out the wave function, allowing one to observe the dissipation-induced correlations with simple measurements. Beyond the on-site model, we also show that a generalised model containing nearest-neighbour dissipative interaction can be engineered and probed in the proposed setup. P hotonic lattices, an array of optical waveguides, have recently emerged as a successful experimental platform to emulate diverse physical phenomena. Most of the works in this field focus on single-particle phenomena, where examples include optical Bloch oscillations of various kinds 1-5 , continuous-time random walks 6 , Anderson localisation 7-9 , dynamic localisation 10 , and dynamic band collapse 11. Simulations of relativistic equations and related effects 12 , such as photonic Zitterbewegung 13 , Klein tunneling 14 , and random mass Dirac model 15 have also been performed, including the simulation of unphysical Majorana equation 16. However, it has been shown that phenomena involving more than one particle can also be simulated in waveguide arrays 17,18. In particular, one can simulate the physics of two interacting particles using two-dimensional (2D) square arrays of linear waveguides along with classical light 19,20 , allowing even richer physics such as Bloch oscillations of correlated particles 21 , fractional Bloch oscillations 22 , and Anderson localisation of two interacting bosons 23 to be observed in photonic lattices. In all of the examples above, dissipation is either an adverse effect that destroys the relevant effect or one that does not play a significant role. However, recent studies have shown that decoherence or dissipation can actually be the main source of non-trivial quantum effects. In the case of optical systems, losses have been deliberately introduced to realise parity-time symmetric systems 24-27 , whereas in an optomechanical system it was shown that it is possible to generate the squeezed state by using dissipation 28. In optical lattices, strong inelastic collisions were used to inhibit particle losses and drive the system into a strongly correlated regime 29-31. There, the two-body inelastic collisions are induced by creating molecules using Feshbach resonance, whereas one-body losses are negligible due to the stability of the system and the absence of thermal background of particles. In this work, we show for the first time that an essential part of such dissipation-induced physics can be simulated using a linear 2D waveguide structure, and moreover using only classical light. Our proposed waveguide simulator allows for highly-tunable effective two-body dissipation rate while having no effective single body losses, making it an excellent candidate to simulate the non-trivial physics induced by strong two-body dissipation. We first introduce a connection between the photonic lattice system and two-body dissipative Bose-Hubbard system, which holds in the two-particle sector. We then discuss how the proposed system allows visualisation of the wave function and relevant observables, and use the fact to illustrate dissipation-induced physics. Interestingly, we find that an effective Hamiltonian description is completely equivalent to the master equation description in the proposed system. The versatility of the proposed setup is highlighted by introducing a generalised model that goes beyond the on-site dissipative Bose-Hubbard model, whose signatures are briefly examined.

Advances In Atomic, Molecular, and Optical Physics, 2013

Ultracold atoms uniformly filling an optical lattice can be treated like an artificial crystal. An implementation including the atomic occupation of a single excited atomic state can be represented by a two-component Bose-Hubbard model. Its phase diagram at zero temperature exhibits a quantum phase transition from a superfluid to a Mott insulator phase. The dynamics of electronic excitations governed by electrostatic dipole-dipole interactions in the ordered regime can be well described by wave-like collective excitations called excitons. Here we present an extensive study of such excitons for a wide range of optical lattice geometries and of different dimensionality including boundary effects in finite lattices. As they are coupled to the free space radiation field, their decay depends on the lattice geometry, polarization and lattice constant. Their lifetimes can vary over many orders of magnitude from metastable propagation to superradiant decay. Particularly strong effects occur in one dimensional atomic chains coupled to tapered optical fibers where free space emission can be completely suppressed and only a superradiant interaction with the fiber modes takes place. We show that coherent transfer of excitons among spatially separated optical lattices can be controlled and represents a promising candidate for quantum information transfer. For an optical lattice within a cavity the excitons are coupled to cavity photons and the resulting collective cavity QED model can be efficiently formulated in terms of polaritons as elementary excitations. Their properties are explicitly calculated for different lattices and they constitute a non-destructive monitoring tool for important system properties as e.g. the atomic quantum statistics. Even the formation of bound states and molecules in optical lattices manifests itself in modified polariton properties as e.g. an anisotropic optical spectrum. Partial dissipation of the exciton energy in the lattice leads to heating, which can be microscopically understood through a mechanism transferring atoms into higher Bloch bands via a resonant excitation transfer among neighboring lattice sites. The presence of lattice defects like vacancies in the Mott insulator induces a characteristic scattering of polaritons, which can be optically observed to monitor the lattice integrity. Our models can be applied to simulate and understand corresponding collective phenomena in solid crystals, where many effects are often masked by noise and disorder.

Physical Review A, 1998

We study the means to prepare and coherently manipulate atomic wave packets in optical lattices, with particular emphasis on alkali atoms in the far-detuned limit. We derive a general, basis independent expression for the lattice operator, and show that its off-diagonal elements can be tailored to couple the vibrational manifolds of separate magnetic sublevels. Using these couplings one can evolve the state of a trapped atom in a quantum coherent fashion, and prepare pure quantum states by resolved-sideband Raman cooling. We explore the use of atoms bound in optical lattices to study quantum tunneling and the generation of macroscopic superposition states in a double-well potential. Far-off-resonance optical potentials lend themselves particularly well to reservoir engineering via well controlled fluctuations in the potential, making the atom/lattice system attractive for the study of decoherence and the connection between classical and quantum physics.

EPL (Europhysics Letters), 2008

We study electronic excitations of a degenerate gas of atoms trapped in pairs in an optical lattice. Local dipole-dipole interactions produce a long lived antisymmetric and a short lived symmetric superposition of individual atomic excitations as the lowest internal on-site excitations. Due to the much larger dipole moment the symmetric states couple efficiently to neighbouring lattice sites and can be well represented by Frenkel excitons, while the antisymmetric dark states stay localized. Within a cavity only symmetric states couple to cavity photons inducing long range interactions to form polaritons. We calculate their dispersion curves as well as cavity transmission and reflection spectra to observe them. For a lattice with aspherical sites bright and dark states get mixed and their relative excitation energies depend on photon polarizations. The system should allow to study new types of solid state phenomena in atom filled optical lattices.

Journal of the Optical Society of America B, 2014

We study the propagation of non-classical light through arrays of coupled linear photonic waveguides and introduce some sets of refractive indices and coupling parameters that provide a closed form propagator in terms of orthogonal polynomials. We present propagation examples of non-classical states of light: single photon, coherent state, path-entangled state and two-mode squeezed vacuum impinging into two-waveguide couplers and a photonic lattice producing coherent transport.

Optics Express, 2013

The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically simulates the interaction of a single two-level system with a quantized field under field nonlinearities and nonlinear couplings as long as the quantum optics model conserves parity. We describe how to reconstruct the mean value of quantum optics measurements, such as photon number and atomic energy excitation, from the intensity and from the field, such as von Neumann entropy and fidelity, at the output of the photonic lattices. We discuss how typical initial states involving coherent or displaced Fock fields can be engineered from recently discussed Glauber-Fock lattices. As an example, the Buck-Sukumar model, where the coupling depends on the intensity of the field, is classically simulated for separable and entangled initial states.

1979

We develop and apply a Hamiltonian variational approach to the study of quantum electrodynamics formulated on a spatial lattice in both 2+1 and 3+1 dimensions. Two lattice versions of QED are considered: a non-compact version which reproduces the physics of continuum QED, and a compact version constructed in correspondence with lattice formulations of non-Abelian theories. Our focus is on photon dynamics with charged particles treated in the static limit. We are especially interested in the nonperturbative aspects of the solutions in the weak-coupling region in order to clarify and establish aspects of confinement. In particular we find, in accord with Polyakov, that the compact QED leads to linear confinement for any nonvanishing coupling, no matter how small, in 2+1 dimensions, but that a phase transition to an unconfined phase for sufficiently weak couplings occurs in 3+1 dimensions. We identify and describe the causes of confinement.

Physical Review A

We study the dynamics of nonlinear photonic lattices driven by two-photon parametric processes. By means of matrix-product-state based calculations, we show that a quantum many-body state with long-range hidden order can be generated from the vacuum. This order resembles that characterizing the Haldane insulator. A possible explanation highlighting the role of the symmetry of the drive, and the effect of photon loss are discussed. An implementation based in superconducting circuits is proposed and analyzed

Nature, 2006

Throughout physics, stable composite objects are usually formed via attractive forces, which allow the constituents to lower their energy by binding together. Repulsive forces separate particles in free space. However, in a structured environment such as a periodic potential and in the absence of dissipation, stable composite objects can exist even for repulsive interactions. Here we report on the first observation of such an exotic bound state, comprised of a pair of ultracold atoms in an optical lattice. Consistent with our theoretical analysis, these repulsively bound pairs exhibit long lifetimes, even under collisions with one another. Signatures of the pairs are also recognised in the characteristic momentum distribution and through spectroscopic measurements. There is no analogue in traditional condensed matter systems of such repulsively bound pairs, due to the presence of strong decay channels. These results exemplify on a new level the strong correspondence between the optical lattice physics of ultracold bosonic atoms and the Bose-Hubbard model[1, 2], a correspondence which is vital for future applications of these systems to the study of strongly correlated condensed matter systems and to quantum information.