Microcavity exciton-polaritons have emerged as an excellent platform for realizing quantum phases of matter, owing to their ability to undergo non-equilibrium Bose-Einstein condensation. Here, we show that the interplay between multiple quantized levels in microcavities and polariton nonlinearity drives the emergence of unconventional phases. Specifically, we demonstrate that intra-site quantization in microcavity polariton lattices—manifested as multiple energy levels in strongly confined sites—provides a route to manipulating these phases. We show that nonlinear interactions transfer population into excited onsite energy levels, acting as an intrinsic dynamical channel that controls coherence across the lattice. While weak nonlinearity confines polaritons to the lowest mode, yielding a robust superfluid phase with broken U(1) symmetry, strong nonlinearity induces phase diffusion through inter-level mixing. This dynamically generated fluctuation suppresses global phase coherence and drives the system into a dynamical Bose-insulating phase. Transitions between these phases occur either as a non-equilibrium phase transition or a sharp crossover. This study investigates the destruction of global order in a non-equilibrium condensate within a lattice featuring onsite quantized energy levels. Long-range fluctuations suppress superfluid stiffness and the condensate fraction, while persistent local order reveals a dynamical Bose-insulating state.
Microcavity exciton-polaritons have emerged as an excellent platform for realizing quantum phases of matter, owing to their ability to undergo non-equilibrium Bose-Einstein condensation. Here, we show that the interplay between multiple quantized levels in microcavities and polariton nonlinearity drives the emergence of unconventional phases. Specifically, we demonstrate that intra-site quantization in microcavity polariton lattices—manifested as multiple energy levels in strongly confined sites—provides a route to manipulating these phases. We show that nonlinear interactions transfer population into excited onsite energy levels, acting as an intrinsic dynamical channel that controls coherence across the lattice. While weak nonlinearity confines polaritons to the lowest mode, yielding a robust superfluid phase with broken U(1) symmetry, strong nonlinearity induces phase diffusion through inter-level mixing. This dynamically generated fluctuation suppresses global phase coherence and drives the system into a dynamical Bose-insulating phase. Transitions between these phases occur either as a non-equilibrium phase transition or a sharp crossover. This study investigates the destruction of global order in a non-equilibrium condensate within a lattice featuring onsite quantized energy levels. Long-range fluctuations suppress superfluid stiffness and the condensate fraction, while persistent local order reveals a dynamical Bose-insulating state.
We demonstrate that Hilbert-space quantization in polariton lattices-manifested as multiple quantized energy levels in strongly confined sites-provides an unconventional route to realizing and manipulating different quantum phases. We show that nonlinear interactions transfer population into excited on-site quantum levels, which acts as an intrinsic dynamical channel controlling quantum coherence across the lattice. While weak nonlinearity confines polaritons to the lowest mode, yielding a robust superfluid phase with broken U(1) symmetry, strong nonlinearity induces phase diffusion through inter-level mixing. This dynamically generated fluctuations suppress global phase coherence and drives the system into a dynamical Bose-insulating phase. The changes between these phases occurs either as a nonequilibrium phase transition or a sharp crossover.
Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity is a macroscopically populated coherent quantum state subject to concurrent pumping and decay. Debates about the fundamental nature of the condensed phase in this open quantum system still persist. Here, we gain a new insight into the spontaneous condensation process by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in the single-shot optical excitation regime, without averaging over multiple condensate realisations. In this highly non-stationary regime, a condensate is strongly influenced by the `hot' incoherent reservoir, and reservoir depletion is critical for the transition to the ground energy and momentum state. Condensates formed by more photonic exciton polaritons exhibit dramatic reservoir-induced density filamentation and shot-to-shot fluctuations. In contrast, condensates of more excitonic quasiparticles display smooth density and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study formation of macroscopic phase coherence during a quantum phase transition in a solid state system.
Bose-Einstein condensate (BEC) is a new state of matter, experimentally realized in a dilute alkali gas of weakly interacting bosons. The gas is cooled to very low temperatures, of the order of nano-Kelvin, at which point a large fraction of the atoms occupy the lowest quantum state. Under such conditions, the quantum effects become apparent on a macroscopic scale. Many fundamental ideas
of quantum mechanics have been realized and proven to be true in experiments,
by studying the Bose-Einstein condensates. Amongst them, the observation of
macroscopic matter wave interference, the creation of vortices, dark and bright
solitons etc, find special mention. The dynamics of this system in presence of an
optical lattice reveals a superfluid to Mott insulator quantum phase transition.
This has opened a new avenue for research on BEC and its applications. From
a theoretical standpoint, the dynamics of BEC can be described by means of an
effective mean-field theory. This formalism is much simpler than the many-body
Schr¨odinger equation and based on a classical nonlinear evolution equation, known
as Gross-Pitaevskii equation. The nonlinear nature of the GPE leads to several interesting phenomena like soliton propagation, vortices, four wave mixing etc.,
which are closely related to nonlinear fiber optics.
The present thesis deals with nonlinear excitations and different phases of BEC
and is organized as follows: after a brief introduction, in chapter two, we start
with BEC in a one-dimensional shallow optical lattice, experiencing both cubic
and quintic nonlinearity. A superfluid density wave, of twice the periodicity of
lattice potential, is identified. This indicates matter redistribution, where atoms
from neighbouring sites have been depleted leading to a density wave behaviour.
Interestingly, it ceases to exist when only one of these interactions is operative.
We predict the loss of superfluidity through a classical dynamical phase transition,
where modulational instability leads to the loss of phase coherence. In presence
of pure two-body interaction, the superfluid density shows a periodicity commensurate
with the lattice potential. Apart from the superfluid state, a density wave
insulating phase is also found to exist, possessing two frequency modulations commensurate
with the lattice potential. A dynamical phase transition connects the
superfluid phase with an insulating phase, which in turn, is connected with the
density wave insulating phase. The solutions are found to be marginally stable, as
per the Vakhitov-Kolokolov (VK) criterion.
Chapter three describes the dynamics of the atomic-molecular Bose-Einstein
condensate (AMBEC) by mean-field Gross-Pitaevskii equation (GPE), taking into
account the atom-molecular interaction, as well as atom-molecule inter-conversion.
The two-body atom-atom, atom-molecule and molecule-molecule interactions are
analogous to the cubic nonlinearity of the standard GPE, whereas, the quadratic
nonlinear term arising from the inter-conversion between atoms and molecules is
identical to the scenario in strongly coupled BEC in one dimension. The presence
of both weak and strong interactions adds further richness to this system. We
find the molecular BEC possesses a complex dark (grey) soliton, while the atomic condensate is a bright one. The energy and momentum of this system is computed
in order to see the effect of the both weak and strong interactions on Lieb mode
profile and compare it with the pure atomic condensate profile. Another class
of solutions exist in this system, where both atomic and molecular condensates
possess bright solitons.
In chapter four, we investigate the effect of a harmonic trap on the dynamics
of grey solitons in Bose-Einstein condensates. It is observed that, these nonlinear
excitations of the cigar-shaped Bose-Einstein condensate have strong coupling
with the trap at low momenta and hence can be effectively isolated from the
Bogoliubov sound modes, which respond weakly to harmonic confinement. This
strong coupling with the trap also makes the grey soliton amenable for control and
manipulation through trap modulation and temporal variation of the two-body interaction.
We have shown that in presence of an expulsive oscillator trap, the grey
soliton gets amplified, while having a compression in its width. Exact solutions are
also obtained in case of the two component Bose-Einstein condensates (TBECs),
where one component is a grey soliton and the other a bright one. The presence
of the trap and inter-species interaction significantly affects the grey soliton dynamics.
Similar to the single component, in the present case, we have shown that
both grey and bright soliton can be compressed simultaneously. A detailed study
of the energy and momentum of the soliton is reported, in order to find the effect
of the trap on the Lieb mode.
In chapter five, we study a BEC-defect complex in a quasi-one dimensional
scenario, where the defect atom moves in the condensate with constant velocity.
Explicit solutions of the coupled mean-field equations, describing defect-grey soliton
dynamics are obtained, demonstrating the coexistence of grey soliton and a
localized defect. Unlike the case of dark soliton, where the defect trapping center
has vanishing superfluid density, the moving grey soliton necessarily possesses a finite superfluid component at the defect location. The presence of the defect can
lower the grey soliton’s maximum velocity, as compared to the defect free case,
where the maximum velocity is the sound velocity. We have also carried out the
stability analysis of the obtained solutions using renormalized momentum formalism
and Vakhitov-Kolokolov criteria and find that the obtained solutions are stable
through both the methods. The grey soliton’s energy gets substantially modified
through its interaction with the defect, opening up the possibility of its control
through defect dynamics.
Chapter six describes a parametrically forced Bose-Einstein condensate in the
presence of a general moving optical lattice. The interaction between the atoms in
the condensate and the time dependent lattice potential leads to a novel propagating
superfluid matter wave, which can be controlled through chirp management.
This system, when placed in a trap, accelerates and undergoes rapid nonlinear
compression, controlled by the chirp. The density achieves its maximum, when
the matter wave changes direction. It is also shown that this system exhibits dynamical
superfluid insulator transition, where superfluidity breaks down and the
condensate transits to an insulating phase. The stability has been investigated
using Vakhitov-Kolokolov criterion and found that it depends on the chirp, as well
as on the nature of the atom-atom interaction. The exact expression for energy
is obtained and analyzed in detail to gain physical understanding of the chirp
management of the sinusoidal excitations and also the dynamical phase transition.
We review, aiming at an audience of final year undergraduates, the phenomena observed in, and properties of, microcavity exciton–polariton condensates. These are condensates of mixed light and matter, consisting of superpositions of photons in semiconductor microcavities and excitons in quantum wells. Because of the imperfect confinement of the photon component, exciton–polaritons have a finite lifetime, and have to be continuously re-populated. Therefore, exciton–polariton condensates lie somewhere between equilibrium Bose–Einstein condensates and lasers. We review in particular the evidence for condensation, the coherence properties studied experimentally, and the wide variety of spatial structures either observed or predicted to exist in exciton–polariton condensates, including quantised vortices and other coherent structures. We also discuss the question of superfluidity in a non-equilibrium system, reviewing both the experimental attempts to investigate superfluidity to date, and the theoretical suggestions of how it may be further elucidated.
Bose-Einstein condensates of exciton-polaritons in inorganic semiconductor microcavities are known to possess strong interparticle interactions attributed to their excitonic component. The interactions play a crucial role in the nonlinear dynamics of such systems and can be witnessed as the high energy shift of polariton states. However, the localised nature of Frenkel excitons in strongly coupled organic microcavities precludes interparticle Coulomb exchange-interactions that affect nonlinear dynamics and change mechanisms of polariton energy shifts accordingly. We have scrutinized the origins of energy shifts in connection with nonlinear dynamics in Frenkel exciton-polariton condensates and examined the possible contributions: intracavity optical Kerr-effect, gain-induced frequency pulling, polariton interactions and effects related to saturation of optical transitions for "dark"- and "bright" molecules [1]. Unlike the conventional strongly coupled semiconductor microcavities, we have shown that nonlinear interactions within the condensate do not rely on polariton interactions but instead originated from Pauli-blocking principle forbidding double excitation of the same molecular states. We have developed a theoretical model explaining the omnipresent energy shift of the condensate wavefunction together with its spectral and polarization features at the BEC transition in a consistent way. The crucial role of intermolecular energy transfer and “dark” exciton reservoir has been demonstrated for the first time. We believe the principles explored in this work are relevant to other systems exhibiting strong coupling of Frenkel excitons with a cavity mode, regardless of a cavity type, whether one dealing with Fabry-Perot cavities or plasmonic nanocavities etc and; therefore, provide general insight on nonlinear phenomena in composite light-matter condensates. [1] T. Yagafarov, D. Sannikov, A. Zasedatelev, K. Georgiou, A. Baranikov, O. Kyriienko, I. Shelykh, L. Gai, Z. Shen, D. G. Lidzey, P. Lagoudakis, Mechanisms of blueshifts in organic polariton condensates, Commun Phys 3, 18 (2020). https://doi.org/10.1038/s42005-019-0278-6
The possible existence of quantum crystals phase of polariton condensate in two-dimensional microcavity polariton was studied by using mean-field method for bosons at zero temperature. In this study, we observe the supersolid crystallized (hexagonal, square) and a quantized winding number of the phase in a regime of strong- field interaction in rotating exciton–polariton condensates. First, the ground state of the condensate was found; and the solution was further extended for dynamics state to reach the equilibrium steady-state as well as their density profile and energy diagrams. The supersolid crystal is the result of the considerable deviation induced by the interaction of polaritons of both ground and dynamic states of a dressed dipolar Bose–Einstein condensate. Here, the researchers demonstrated the formation of a hexagonal lattice in the nonlinear regime at high polariton-density where polariton–polariton interactions dominate the behavior of the system. It was identified that stability regimes for ground state increases as the polariton–polariton interaction strength increases. The phase diagram for the stable vortex state will be useful for conducting experimental and theoretical studies on rotating dipolar quantum gases and many other exotic systems.