Collective-Coordinate Dynamics and Radiative Decoherence in a Driven-Dissipative Polariton CondensateGeometric constraints on centre-of-mass path coherence and a numerical test of self-confinement This paper asks whether a room-temperature driven-dissipative exciton-polariton condensate can supply a localized collective coordinate able to occupy a resolvable two-path superposition. For the platform considered and for ordinary radiative coupling, the answer is negative for two independent reasons, and the paper states precisely where the formal construction holds and where its physical realization fails. Radiative which-path decoherence. Treating the condensate as an open system with a mode-resolved loss channel, the coherence between two localized branch states decays at ΓCOM = Nγ[1 − Re χ(d)], where χ(d) is the overlap of the photon states emitted by the two branches. The controlling variable is environmental distinguishability rather than mechanical recoil: a photon that displaces the centre of mass by a negligible amount can still record, at full strength, which branch the emitter occupied. Where ordinary out-coupling preserves transverse-mode information, two requirements act on the same length scale and conflict — branch resolvability requires a separation of several core widths, indistinguishability requires a separation well below one — so that, for a sech profile and the working convention d ≳ 3ξ, the dimensionless ratio ΓCOM/(Nγ) is bounded below by about 0.7. The coefficient is geometric; the absolute rate retains its dependence on N and γ. Numerical test of self-confinement. The operating point inferred from the measured group velocity on the CsPbBr3 microwire platform lies in the positive-effective-mass regime, where repulsive polariton interactions do not support a bright soliton. A free-propagation integration anchored to that regime shows a packet seeded at the analytic width broadening from 2.2 µm to 25.8 µm over 6 ps, so the proposed self-confined realization is not present there. A negative-mass run is retained only as a control of the propagation solver. Corrected collective wavelength. The de Broglie wavelength of the collective coordinate follows from the aggregate mass M* = N mLP, not from the single-polariton value: λCOM = h/(M*vg) = λLP/N ≈ 0.11 nm. The corresponding Fraunhofer scale far exceeds the demonstrated 60 µm propagation length, so no far-field centre-of-mass double-slit geometry is proposed for this platform. Supporting these results, the collective-coordinate construction is retained as a conditional formal sector for a rigid bright soliton: translational symmetry protects free motion exactly, the Kohn conditions protect harmonic centre-of-mass motion, and a hydrodynamic Madelung cross-check reproduces the same statement independently. In the aperture region the adiabaticity parameter is of order unity on the platform considered, so no perturbative mass-renormalization coefficient is assigned there. The paper distinguishes first-order field coherence, which a driven condensate can maintain and which is experimentally measured, from coherence between two centre-of-mass configurations, which the radiative channel destroys. The argument is independent of any interpretation of quantum mechanics. Engineering of the output reservoir so that the two branches emit into nearly indistinguishable environmental modes is identified as the route by which radiative which-path decoherence could be suppressed. Changes in version 2.0 Version 2.0 revises the central claim of version 1.0 and should be read in place of it. The title and the subject of the paper have both changed. Retracted. The suppressed decoherence rate of version 1.0 and the 1/N estimate on which it rested. That estimate measures the back-action of a quantum jump on the mean position; it does not measure the which-path information deposited in the environment, which scales with the number of constituents rather than against it. The coherence time reported in version 1.0, and the transit-time margin derived from it, do not hold. Withdrawn. The claim that the structure traverses a double slit in a coherent superposition of paths; the claim that a transition between interpretations of quantum mechanics emerges as a necessary structure of the dynamics; the reduced fringe visibility previously advanced as the primary experimental signature, which is a property of the order parameter rather than of a path superposition; and the self-confinement property, shown numerically not to hold at the operating point of the platform. The acronym under which the construction was introduced is not used further. Removed from scope. The admissibility layer and the interpretive material associated with it. This version is self-contained within condensed-matter physics and quantum decoherence, and its results depend on no unpublished work. Corrected. Parameter provenance. Version 1.0 combined quantities measured on four distinct platforms and conflated the cavity photon lifetime, the polariton lifetime and the first-order coherence time. All platform inputs are now drawn from one system and tabulated with operational definition, origin and status as measured, derived or chosen. The de Broglie wavelength of the collective coordinate is corrected. The description of the soliton solution set as a symplectic manifold is weakened to a finite-dimensional collective-coordinate manifold, and the claim to a first explicit formulation of the mapping as an identity is withdrawn; the Ehrenfest theorem is stated as a consistency check rather than as the derivation. Retained. The strong-coupling analysis, the conditional collective-coordinate reduction, the exact symmetry sectors with their hydrodynamic cross-check, and the parametric relation between mass and nonlinearity, the last now confirmed against a measurement on the platform.
Collective-Coordinate Dynamics and Radiative Decoherence in a Driven-Dissipative Polariton CondensateGeometric constraints on centre-of-mass path coherence and a numerical test of self-confinement This paper asks whether a room-temperature driven-dissipative exciton-polariton condensate can supply a localized collective coordinate able to occupy a resolvable two-path superposition. For the platform considered and for ordinary radiative coupling, the answer is negative for two independent reasons, and the paper states precisely where the formal construction holds and where its physical realization fails. Radiative which-path decoherence. Treating the condensate as an open system with a mode-resolved loss channel, the coherence between two localized branch states decays at ΓCOM = Nγ[1 − Re χ(d)], where χ(d) is the overlap of the photon states emitted by the two branches. The controlling variable is environmental distinguishability rather than mechanical recoil: a photon that displaces the centre of mass by a negligible amount can still record, at full strength, which branch the emitter occupied. Where ordinary out-coupling preserves transverse-mode information, two requirements act on the same length scale and conflict — branch resolvability requires a separation of several core widths, indistinguishability requires a separation well below one — so that, for a sech profile and the working convention d ≳ 3ξ, the dimensionless ratio ΓCOM/(Nγ) is bounded below by about 0.7. The coefficient is geometric; the absolute rate retains its dependence on N and γ. Numerical test of self-confinement. The operating point inferred from the measured group velocity on the CsPbBr3 microwire platform lies in the positive-effective-mass regime, where repulsive polariton interactions do not support a bright soliton. A free-propagation integration anchored to that regime shows a packet seeded at the analytic width broadening from 2.2 µm to 25.8 µm over 6 ps, so the proposed self-confined realization is not present there. A negative-mass run is retained only as a control of the propagation solver. Corrected collective wavelength. The de Broglie wavelength of the collective coordinate follows from the aggregate mass M* = N mLP, not from the single-polariton value: λCOM = h/(M*vg) = λLP/N ≈ 0.11 nm. The corresponding Fraunhofer scale far exceeds the demonstrated 60 µm propagation length, so no far-field centre-of-mass double-slit geometry is proposed for this platform. Supporting these results, the collective-coordinate construction is retained as a conditional formal sector for a rigid bright soliton: translational symmetry protects free motion exactly, the Kohn conditions protect harmonic centre-of-mass motion, and a hydrodynamic Madelung cross-check reproduces the same statement independently. In the aperture region the adiabaticity parameter is of order unity on the platform considered, so no perturbative mass-renormalization coefficient is assigned there. The paper distinguishes first-order field coherence, which a driven condensate can maintain and which is experimentally measured, from coherence between two centre-of-mass configurations, which the radiative channel destroys. The argument is independent of any interpretation of quantum mechanics. Engineering of the output reservoir so that the two branches emit into nearly indistinguishable environmental modes is identified as the route by which radiative which-path decoherence could be suppressed. Changes in version 2.0 Version 2.0 revises the central claim of version 1.0 and should be read in place of it. The title and the subject of the paper have both changed. Retracted. The suppressed decoherence rate of version 1.0 and the 1/N estimate on which it rested. That estimate measures the back-action of a quantum jump on the mean position; it does not measure the which-path information deposited in the environment, which scales with the number of constituents rather than against it. The coherence time reported in version 1.0, and the transit-time margin derived from it, do not hold. Withdrawn. The claim that the structure traverses a double slit in a coherent superposition of paths; the claim that a transition between interpretations of quantum mechanics emerges as a necessary structure of the dynamics; the reduced fringe visibility previously advanced as the primary experimental signature, which is a property of the order parameter rather than of a path superposition; and the self-confinement property, shown numerically not to hold at the operating point of the platform. The acronym under which the construction was introduced is not used further. Removed from scope. The admissibility layer and the interpretive material associated with it. This version is self-contained within condensed-matter physics and quantum decoherence, and its results depend on no unpublished work. Corrected. Parameter provenance. Version 1.0 combined quantities measured on four distinct platforms and conflated the cavity photon lifetime, the polariton lifetime and the first-order coherence time. All platform inputs are now drawn from one system and tabulated with operational definition, origin and status as measured, derived or chosen. The de Broglie wavelength of the collective coordinate is corrected. The description of the soliton solution set as a symplectic manifold is weakened to a finite-dimensional collective-coordinate manifold, and the claim to a first explicit formulation of the mapping as an identity is withdrawn; the Ehrenfest theorem is stated as a consistency check rather than as the derivation. Retained. The strong-coupling analysis, the conditional collective-coordinate reduction, the exact symmetry sectors with their hydrodynamic cross-check, and the parametric relation between mass and nonlinearity, the last now confirmed against a measurement on the platform.
Microcavity-polaritons are quasi-particles formed when light and matter excitations couple strongly in cavities that have confinement lengths similar to the wavelength of light. Polariton’s light e↵ective mass, due to the photonic component, in conjunction with their composite boson nature, allows a transition into a macroscopically occupied quantum degenerate state (polariton condensate) for temperatures ranging from 4K up to room temperature. Due to the exciton reservoirs produced under non-resonant excitation and polariton’s strong interparticle interactions (originating from their matter component) potential landscapes for the polaritons can be sculpted with the non-resonant laser beam(s) pumping the system. The work presented in this thesis is specifically concerned with inorganic polariton condensates in optically imprinted potential landscapes. With annular excitation geometries it is possible to form optically trapped polariton condensates, where the condensate is spatially delocalised from the exciton reservoir. Implementing this optical trap geometry, the first all-optical polariton bistability under non-resonant excitation is demonstrated in the spinor of the condensate. Furthermore, the separation from the exciton reservoir results in significant enhancement of the coherence properties. First order coherence times exceeding 1.5ns are demonstrated for the optical trap excitation geometry; whilst excitation regimes where the condensate overlaps the reservoir demonstrate sub 100ps coherence times. For narrow Gaussian excitation geometries, the spatial overlap of the condensate and the reservoir results in polaritons ballistically propagating away from pump with a well defined in-plane wavevector. Utilising this inherent in-plane propagation, two freely expanding polariton condensates (a polariton dyad) are shown to remain coupled, even for separation distances exceeding 100μm. Through an in-depth experimental and theoretical investigation of the polariton dyad, it is determined that it is critically important to account for the finite propagation time of polaritons from one condensate centre to the other (i.e. the coupling is time-delayed). The experimental work in this thesis is then concluded by introducing all-optical polariton band structure engineering. Utilising optically imprinted polariton condensates and their exciton reservoirs to both create and image the band structures. In addition to the experimental results, experimental procedures and analysis techniques, that have been developed and implemented to facilitate the research, are presented.
The central theme of this thesis is that of coherence in bosonic matter-wave fields. Analogous to optical coherence; the measure of the capacity of a photonic beam to produce fringes upon interference; matter-wave coherence is in many ways the defining characteristic of the BEC phase of identical massive bosons. Its study therefore plays a critical role in the quest to better understand the physics of ultra-cold quantum gases, which has been the goal of this research. This work approaches coherence from a number of different angles and is for this reason presented in two parts. The first of these delves into the physics of perfectly coherent matterwave fields which are adequately described by ‘mean field’ equations, while the second is devoted to origins and repercussions of the diminished coherence evident in actual atom laser experiments. The presentation of the original work of this project begins with a detailed study of the interaction between an atomic and a molecular condensate, coherently coupled at zero temperature via one of several possible mechanisms (a Feshbach resonance, for example) in three spatial dimensions. Despite the presence of repulsive scattering interaction between the atoms, the mean-field equations of motion are known to support bright solitary waves — time-independent solutions which remain localised even in the absence of a trapping potential. (These solutions are the matter-wave analogue of spatio-temporal solitons in quadratic nonlinear media, but can also represent stationary states of the Schr¨odinger-Newton equations describing bosons interacting via a gravitational field.) Ignoring all interactions save the repulsive inter-atomic scattering mentioned, a variational ansatz approach is employed to analytically approximate these stationary solutions using Gaussian density distributions of the atomic and molecular clouds. By evolving these approximate solutions numerically, a comprehensive map of the accessible parameter space is constructed, showing primarily stable localised propagation. Parameter space regions where the approximate Gaussian solutions display strong ‘breathing’ oscillations are identified, and a modified ansatz having exponentially decaying tails is found to dramatically reduce the amplitude of these oscillations. Finally, by seeding a numerical relaxation algorithm with our Gaussian solutions, we find that the only parameter space region in which the approximate solutions diffuse under propagation is also devoid of exact localised stationary solutions. The discussion then proceeds beyond the scope of mean field theory, and turns to a detailed treatment of the quantum mechanical observable corresponding to the centre of mass of systems of identical particles. Firstly, careful consideration is given to its operational definition in the presence of fluctuating particle numbers. Possible pitfalls due to naive approximations when the number fluctuations are large are also addressed. Attention is then given to the fundamental quantum noise associated with this variable, which provides a physical mechanism for diminished first order coherence in degenerate Bose gases, even at zero temperature. Characteristic lower bounds (standard quantum limits) to the resulting mean position uncertainty are identified both for systems of identical bosons and identical fermions with comparable density profiles. Interestingly, fermions are found to have an intrinsically lower mean-position uncertainty than bosons, a fact which is attributed to the action of Pauli repulsion between atoms confined to a fixed density distribution. The results of numerical simulations of the exact quantum evolution of mean position variance are then presented. These demonstrate firstly the quantum diffusion of the mean position of one dimensional matter-wave solitons and secondly the evolution of variance in the centre of mass of a Bose gas undergoing forced evaporative cooling. Finally, attention is paid to the fact that the Penrose-Onsager criterion, which essentially equates Bose condensation with perfect first-order matter-wave coherence, fails to correctly detect the presence of BEC when a priori knowledge of the exact condensate mode is imperfect or unavailable. Insight is gained by drawing analogies between this criterion and entropic measures of entanglement between particular system subspaces. This motivates employment of the concept of entanglement of formation as a means to providing a more accurate measure of condensation in the general case of mixed system states. Unfortunately, this new measure remains adversely sensitive to superpositions of condensate modes. For this reason, alternative criteria based on higher order particle number correlation functions are also proposed.
We review recent results on the coherence and superfluidity of driven dissipative condensates, i.e., systems of weakly interacting nonconserved bosons, such as polariton condensates. The presence of driving and dissipation has dramatically different effects depending on dimensionality and anisotropy. In three dimensions, equilibrium behaviour is recovered at large scales for static correlations, while the dynamical behaviour is altered by the microscopic driving. In two dimensions, for an isotropic system, drive and dissipation destroy the algebraic order that would otherwise exist; however, a sufficiently anisotropic system can still show algebraic phase correlations. We discuss the consequences of this behaviour for recent experiments measuring phase coherence and outline potential measurements that might directly probe superfluidity. Introduction This chapter is dedicated to superfluidity and its relation to Bose-Einstein condensation (BEC), a topic with a long history. Many reviews of the concepts of condensation and superfluidity in thermal equilibrium can be found; see for example Refs. [1, 2, 3, 4]. The focus of this chapter is on how these concepts apply (or fail to apply) to driven dissipative condensates – systems of bosons with a finite lifetime, in which loss is balanced by continuous pumping. We focus entirely on the steady state of such systems, neglecting transient, time-dependent behaviour. Experimentally, the most studied example of a driven dissipative condensate has been microcavity polaritons, an overview of which is given in Ref. [5] and Chapter 4. However, similar issues can arise in many other systems, most obviously photon condensates [6] (see also Chapter 19), magnon condensates [7] (see also Chapters 25–26), and potentially exciton condensates (although typical exciton lifetimes are much longer than for polaritons). Even experiments on cold atoms (see, e.g., Chapter 3) could be driven into a regime in which such physics occurs, when considering continuous loading of atoms balancing threebody losses [8] or atom laser setups [9, 10, 11]. Experiments on polaritons are two-dimensional, and in two dimensions it is particularly important to clearly distinguish three concepts often erroneously treated as equivalent: superfluidity, condensation, and phase coherence. This is because no true Bose-Einstein condensate exists in a homogeneous two-dimensional system.
This paper develops a framework-relative ontology of determinacy. Its core question is not what the world is made of, but what must minimally be accounted for if a stable deter- minate identity is internally self-representing. The primitive and functional core of Version 3.8 is retained: Being, the possibility of distinction, and domain-relative realizability define the sparse primitive basis; coherent self-representation then requires three non-equivalent func- tional questions—Support, Internal Encoding, and Correspondence. Explicit finite witness pairs establish uniform non-determination of each role from the other two in the unrestricted baseline class, while stronger canonical or equivariant subclasses remain open. Version 4.1.1 is a corrective consolidation of Version 4.1 rather than a new upstream on- tology step. It retains the Version 4.0 bridge revision and the Version 4.1 constructional layer. That layer adds the reverse evaluative direction Physics ⇒ Mathematics ⇒ Ontology and records where downstream structures constrain, but do not retroactively constitute, the ontol- ogy. Several previous bridge claims are weakened or rejected. Symmetry classification, tensor factorization, entanglement of a state, and path-dependent dynamics are kept as four distinct mathematical layers. A conditional expectation is treated as a localization map rather than as actualization; a branch instrument defines possible conditional events but does not select one realized branch; and a projection onto admissible spectral sectors is not called conservative dynamics without an independently derived dilation. The causal and propagation bridge is sharpened in two directions. First, a previous can- didate definition of a null relation by vanishing accumulated interval volume is proved degen- erate: every comparable pair admits a chain of links, so that criterion vanishes throughout the causal order. Link ensembles remain useful near-null approximants, but the null sector is therefore a limiting or measure-relative object rather than a pair-local primitive in the de- clared causal-set model. Second, the long-range free-chain calculation at 𝛼 = 2 is separated into two non-commuting limits. The infinite-range spectral symbol has maximal group veloc- ity 𝜋𝐽𝑎, whereas the envelope of finite-cutoff maxima tends to 2𝐽𝑎 Si(𝜋). These are spectral group-velocity statements; a causal signal cone still requires separate Lieb–Robinson-type hy- potheses. Isotropy and a unique physical Lorentz cone remain open. The defect bridge is updated with the completed 𝐾 = 512 data layer of the frozen ratio campaign. All 903 prescribed values of 𝜃 are present with eight branches each; 897 aggregate points are admissible and six lie in a short rejected interval. Neither √ 2 nor 𝜙 is a local or global minimum. The original preregistered primary ratio test nevertheless remains non- evaluable because its 𝐾 = 64 training gate is universally degenerate. Thus 𝐾 = 512 completes a characterization block; it does not retrospectively repair the primary estimator. Provenance registration and cross-platform verification remain pending. Version 4.0 turned Test 28A into an explicit reconstruction audit, and Version 4.1 retains that audit unchanged. For the standard three one-body extractions on ℋ = (C 3 ) ⊗3 , the combined linear map has exact rank 25 and kernel dimension 704. The hidden space splits as 192 two-body plus 512 fully traceless three-body directions; even the full 𝑆3-invariant class retains an exact 156-dimensional hidden sector. The preregistered continuation identifies an exact energy-selected fixed point, the totally antisymmetric state |𝜀⟩, while holonomy and variance objectives yield set-valued argmin correspondences. The historical non-triviality gate is therefore preserved but shown not to be a universal criterion, and no retroactive 𝑉28.4 verdict is declared. A prospectively frozen two-local QPH family provides an exact computer-assisted existence witness: its cycle-phase differential has rank 704/704 on the marginal kernel for the primary family and two preregistered replications, so marginals plus relational cycle phases are locally in- formationally complete in the fixed regularity stratum. Canonical modular-mismatch selectors are then audited rather than assumed. Identical additive qutrit references and every single pure mismatch under exact 𝑆3 protection obey strict capacity/rank no-go bounds. On the protected 156-dimensional domain a physically generated mixed mismatch has sufficient raw capacity but standard phase-only QPH remains incomplete. Exact cumulant analysis explains why order three is the natural next layer: the 𝑆3-hidden sector decomposes as 156 = 36 + 120, and the third connected cumulant is a complete affine coordinate on fibres of fixed proper marginals. A historical preregistered cubic-moment completion is retained only as a delicate T-NUM wit- ness, not as a theorem premise. This is the declared stopping point of the arity/cubic line: selecting one specific cubic observable would require a new independent physical law. Test 28B remains suspended. Version 4.0 added one further macro-level correction, retained in Version 4.1. Causal and conformal structure, transport geometry, stable matter sectors, and quantum correlations are treated as parallel downstream representations of one substrate model, not as a serial matter– space–time chain. A proposed identification of the matter admissibility projector Πadm with spacetime volume is rejected in its literal form: the projector is matter-branch specific, need not be nested under generative updates, and has no canonical finite trace in a type-III con- tinuum. In its place a conditional causal–transport conformal closure theorem is proved. If a causal reconstruction supplies a Lorentzian conformal class and an independent transport limit supplies a positive spatial metric on the same spacelike distribution, the conformal factor is fixed pointwise exactly when the two induced spatial metrics are conformally compatible. A scale-free generalized-eigenvalue defect provides a direct falsifier. The corresponding clock– cone–matter gate is also corrected by conformal weight: frequencies and dimensionful spectral scales have lapse weight one under a pure lapse deformation, whereas spectral ratios, localiza- tion fractions, and dimensionless stability-window coordinates have weight zero. A Tolman– thermal-time comparison is retained only as a relative lapse-profile gate; absolute time units remain open. Version 4.1 introduced a controlled common-substrate realization. Version 4.1.1 corrects its scope: parity alone excludes only an odd or linear mass/source identification with the same signed coordinate; an even law such as 𝑀 ∝ 𝑑 2 is not excluded by parity. On the declared graph Klein–Gordon sector, charge conjugation reverses Noether/gauge-current orientation while leaving mode energy and localization intensity unchanged. A grounded-graph Green- kernel theorem fixes the spatial uniformity of the cross-term sign, while the Coulomb sign itself is conditional on realizing a non-dynamical 𝐴0-type constraint sector; the same kernel in a dynamical scalar sector gives the opposite sign. A separate no-go proves that matter Dirichlet energy alone cannot select a nontrivial interior geometry. A state-selected positive geometry Hessian yields the conditional linear response 𝑦 = 𝐾 −1 𝐸 𝜏 , so weak 𝐶-even stress sources add while 𝐶-odd currents can cancel. The principal new bridge is a conditional stationary common causal–transport–matter con- struction. If one protected center supplies a common base, the transport branch supplies a positive spatial metric ℎ, and several modular/physical clocks agree on one relative lapse 𝑁, then 𝑔CTM = −𝑐 2 *𝑁2𝑑𝑇2 + ℎ has one timelike sign, predicts the same null front for all canonically normalized matter sectors, and fixes its stationary volume element without an additional scalar measure. Different masses and opposite 𝑈(1) representation weights remain lower-order data and do not alter the characteristic cone. The independently reconstructed HSMI conformal class remains a held-out test rather than an input to this construction. A second independent Version 4.1 result supplies a conditional physical law selecting com- plex rank two. A nonzero-Chern line cannot be closed under conjugation at rank one on 𝑆 2 , whereas 𝐿 ⊕ 𝐿¯ is the minimal conjugation-closed carrier; independently, ClC 2 ≃ 𝑀2(C) has minimal irreducible complex module dimension two. The existing odd-Chern defect-link con struction realizes this pair. If its Clifford algebra is physically admissible, the local carrier has 𝑀2(C) qubit kinematics. This is not an assertion that opposite electric charges form a coherent qubit, nor that every particle is a qubit. The resulting Version 4.1.1 is a constrained foundational proposal with a frozen primitive core, stronger positive and negative bridge results, a first common stationary geometry can- didate, an independently motivated minimal rank-two carrier, and a reproducibility-oriented ledger for every step from ontological determinacy toward physics. It also makes the external spin-sign, soft-graviton, equivalence-principle, and mass-budget inputs explicit without treat- ing them as evidence for the ontology.
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.
This work investigates which outcome-like behaviors can arise in closed, momentum-accounted quantum models before any additional irreversible state-selection mechanism is introduced. A hierarchy of conservative controls is developed using a finite-mass beam splitter, explicit record degrees of freedom, conditioned and unconditioned branch histories, nonlinear two-mode many-body dynamics, many-mode record sectors, and recoil-dependent visibility and distinguishability. The analysis shows that several behaviors commonly associated with measurement-like dynamics can be reproduced within the closed models considered here. A finite-mass splitter supports explicit entanglement between recoil and field apparatus while preserving the total momentum ledger. Record formation suppresses reduced-state coherence and produces strongly branch-polarized conditioned histories, while the unconditioned state retains both alternatives. A separate many-body status analysis shows that collective nonlinear dynamics can generate genuine self-trapping and long-lived population imbalance, while the interaction studied becomes branch-independent in the single-excitation sector through Jz2 = I/4. Increasing record complexity can also strongly suppress finite-window recoherence through effective spectral participation and phase structure without introducing nonunitary dynamics. Finally, the finite apparatus degree of freedom that carries recoil is connected directly to branch-state overlap, interference visibility, and optimal path distinguishability, providing a common quantitative description of momentum exchange and which-path information. The results do not constitute a solution to the quantum measurement problem, a derivation of a unique measurement outcome or the Born rule, or a no-go theorem for modified quantum dynamics. Rather, they establish a reproducible control hierarchy: outcome-like behavior should first be tested against closed standard models capable of reproducing the same observable signature before it is interpreted as evidence for an additional irreversible state-selection mechanism. Data and reproducibility: Numerical data, source code, diagnostic outputs, and publication figures supporting the computational controls are available in the associated Zenodo reproducibility archive.