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arXiv:1906.03103

Towards Arbitrary Control of Lattice Interactions in Nonequilibrium Condensates

Kirill P. Kalinin, Natalia G. Berloff

Published Jun 7, 2019• 1 citation
arXivHTMLPDF

Abstract

There is a growing interest in investigating new states of matter using out-of-equilibrium lattice spin models in two dimensions. However, a control of pairwise interactions in such systems has been elusive as due to their nonequilibrium nature they maintain nontrivial particle fluxes even at the steady state. Here we suggest how to overcome this problem and formulate a method for engineering reconfigurable networks of nonequilibrium condensates with control of individual pairwise interactions. Representing spin by condensate phase, the effective two spin interactions are created with nonresonant pumping, are directed with dissipative channels, and are further controlled with dissipative gates. The dissipative barriers are used to block unwanted interactions between condensates. Together, spatial anisotropy of dissipation and pump profiles allow an effective control of sign and intensity of the coupling strength between any two neighboring sites independent of the rest of the spins, which we demonstrate with a two dimensional square lattice of polariton condensates. Experimental realisation of such fully-controllable networks offers great potential for an efficient analog Hamiltonian optimizer and for reservoir computing.

DOI
10.48550/arxiv.1906.03103

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There is a growing interest in investigating new states of matter using out-of-equilibrium lattice spin models in two dimensions. However, a control of pairwise interactions in such systems has been elusive as due to their nonequilibrium nature they maintain nontrivial particle fluxes even at the steady state. Here we suggest how to overcome this problem and formulate a method for engineering reconfigurable networks of nonequilibrium condensates with control of individual pairwise interactions. Representing spin by condensate phase, the effective two spin interactions are created with nonresonant pumping, are directed with dissipative channels, and are further controlled with dissipative gates. The dissipative barriers are used to block unwanted interactions between condensates. Together, spatial anisotropy of dissipation and pump profiles allow an effective control of sign and intensity of the coupling strength between any two neighboring sites independent of the rest of the spins, which we demonstrate with a two dimensional square lattice of polariton condensates. Experimental realisation of such fully-controllable networks offers great potential for an efficient analog Hamiltonian optimizer and for reservoir computing.
Abstract There is a growing interest in investigating new states of matter using out‐of‐equilibrium lattice spin models in two dimensions. However, a control of pairwise interactions in such systems has been elusive as due to their nonequilibrium nature they maintain nontrivial particle fluxes even at the steady state. Here it is suggested how to overcome this problem and formulate a method for engineering reconfigurable networks of nonequilibrium condensates with control of individual pairwise interactions. Representing spin by condensate phase, the effective two spin interactions are created with nonresonant pumping, are directed with dissipative channels, and are further controlled with dissipative gates. The dissipative barriers are used to block unwanted interactions between condensates. Together, spatial anisotropy of dissipation and pump profiles allow an effective control of sign and intensity of the coupling strength between any two neighbouring sites independent of the rest of the spins, which is demonstrated with a 2D square lattice of polariton condensates. Experimental realization of such fully controllable networks offers great potential for reservoir computing, modelling of the systems of coupled oscillators, simulation of the new state of matters, studying the phase transitions in large‐scale systems, and optimization.
There is a growing interest in investigating new states of matter using out-of-equilibrium lattice spin models in two dimensions. However, a control of pairwise interactions in such systems has been elusive as due to their nonequilibrium nature they maintain nontrivial particle fluxes even at the steady state. In article number 1900065 Natalia Berloff and co-workers suggest how to overcome this problem and formulate a method for engineering reconfigurable networks of nonequilibrium condensates with control of individual pairwise interactions.
We demonstrate that multiply coupled spinor polariton condensates can be optically tuned through a sequence of spin-ordered phases by changing the coupling strength between nearest neighbors. For closed four-condensate chains these phases span from ferromagnetic (FM) to antiferromagnetic (AFM), separated by an unexpected crossover phase. This crossover phase is composed of alternating FM-AFM bonds. For larger eight-condensate chains, we show the critical role of spatial inhomogeneities and demonstrate a scheme to overcome them and prepare any desired spin state. Our observations thus demonstrate a fully controllable nonequilibrium spin lattice.
Exciton-polariton Bose-Einstein condensates (BECs) are newly emerged quantum systems that are capable of showing macroscopic quantum phenomena with intrinsic open-dissipative nature. The spatial distribution of the polariton density, without any external potential, can be controlled by the geometric shape of the pumping laser, enabling the investigation of polariton dynamics with topologically non-trivial configurations. Meanwhile, exciton-polaritons have spin degrees of freedom inherited from excitons and photons, making it a candidate for the realization of quantum logic gates. In this thesis, we will investigate theoretically the nonlinear dynamics of exciton-polariton BECs involving both polaritons' spatial degrees of freedom and spin degrees of freedom, and interactions between them. This thesis is organised as follows: In Chapter 1, we will present an overall review of exiton-polariton systems and important properties of polariton BECs and then introduce the dynamical equations with various interactions that will serve as the main theoretical tool for subsequent chapters. Several polariton pumping and trapping techniques appearing in later chapters will also be introduced. In Chapter 2, we will investigate the superfluidity properties of a single-component polariton condensate under an incoherent annular pumping configuration. By studying the stability properties of polariton persistent currents, we find that the persistent currents can exhibit dynamical instability and energetic-like instability according to different parameter region. A stability phase diagram will be given and its relation with the Landau's criterion will be discussed. In Chapter 3, we will investigate the spin dynamics of a two-component polariton condensate under a homogeneous pumping configuration. Owing to the Josephson coupling, there exist multiple steady state solutions that allow of controlled spin state switching. A desynchronized region where there exists no stable steady solution is found. In the desynchronized region, a desynchronized state beating periodically over time can exist, which will serve as a building block of spin waves presented in the next chapter. In Chapter 4, by combining results from the previous two chapters we will investigate generally the nonlinear dynamics of polariton condensates under an annular pumping configuration. The spin-orbit interaction provided by the Josephson coupling supports azimuthon states that have simultaneous modulations in both amplitude and phase. The azimuthon states, when viewed in a different polarization basis, form rotating spin waves that can be referred to as the optical ferris wheel. In Chapter 5, results from previous chapters will be extended to micocavities that support the anisotropic TE-TM splitting interaction. Rotating singularities (small-scale vortices) are found as a result. Their properties and experimental observation techniques will be discussed. Chapter 2-5 provide a theoretical framework for the nonlinear dynamics of polariton condensates. They rely mostly on optical trapping techniques and are ready to be tested in experiments. In Chapter 6, polaritons trapped by an engineered periodic mesa potential will be discussed. We will investigate the band structure of polaritons under the influence of the periodic potential together with discussions on the phase-modulated interference pattern which corresponds to the polariton Talbot patterns observed in experiments.
We present a platform for the simulation of quantum magnetism with full control of interactions between pairs of spins at arbitrary distances in 1D and 2D lattices. In our scheme, two internal atomic states represent a pseudospin for atoms trapped within a photonic crystal waveguide (PCW). With the atomic transition frequency aligned inside a band gap of the PCW, virtual photons mediate coherent spin-spin interactions between lattice sites. To obtain full control of interaction coefficients at arbitrary atom-atom separations, ground-state energy shifts are introduced as a function of distance across the PCW. In conjunction with auxiliary pump fields, spin-exchange versus atom-atom separation can be engineered with arbitrary magnitude and phase, and arranged to introduce nontrivial Berry phases in the spin lattice, thus opening new avenues for realizing topological spin models. We illustrate the broad applicability of our scheme by explicit construction for several well-known spin models.
Classical spin models with discrete or continuous degrees of freedom arise in many studies of complex physical systems. A wide class of hard real-life optimization problems can be formulated as a minimization of a spin Hamiltonian. Here we show how to simulate the discrete Ising and n-state planar Potts models with or without external fields using the physical gain-dissipative platforms with continuous phases, such as lasers and various nonequilibrium Bose-Einstein condensates. The underlying operational principle originates from a combination of resonant and nonresonant pumping. Our results lay grounds for the physical simulations of a broad range of Hamiltonians with complex interactions that can vary in time and space and with combined symmetries.