Continuous Translational Symmetry Research Articles

Quantum lattice models that preserve continuous translation symmetry

Quantum lattice models that preserve continuous translation symmetry

Realization of an inherent time crystal in a dissipative many-body system

Time crystals are many-body states that spontaneously break translation symmetry in time the way that ordinary crystals do in space. While experimental observations have confirmed the existence of discrete or continuous time crystals, these realizations have relied on the utilization of periodic forces or effective modulation through cavity feedback. The original proposal for time crystals is that they would represent self-sustained motions without any external periodicity, but realizing such purely self-generated behavior has not yet been achieved. Here, we provide theoretical and experimental evidence that many-body interactions can give rise to an inherent time crystalline phase. Following a calculation that shows an ensemble of pumped four-level atoms can spontaneously break continuous time translation symmetry, we observe periodic motions in an erbium-doped solid. The inherent time crystal produced by our experiment is self-protected by many-body interactions and has a measured coherence time beyond that of individual erbium ions.

Photonic Dirac cone and topological transition in a moving dielectric slab

The moving media theory is applied to a photonic confined structure which is a continuous dielectric slab waveguide with the uniaxial anisotropy and without the discrete translational symmetry. The moving effect not only brings about non-reciprocity to the whole photonic band structure in the co-moving and counter-moving directions, but also leads to the topological transition of local degenerate points within the band diagram. We demonstrate through calculation that the type-II Dirac point can be turned into type-I Dirac point when the uniaxial slab is moving over certain speed. Our results provide a new approach to regulate the topology of degeneracy for two-dimensional photonic bands in the continuous translational symmetry condition.

Self-ordered supersolid phase beyond Dicke superradiance in a ring cavity

The supersolid phase characterized by the superfluid and long-range spatial periodicity of crystalline order is central to many branches of science ranging from condensed matter physics to ultracold atomic physics. Here we study a self-ordered checkerboard supersolid phase originating from dynamical spin-orbit coupling for a transversely pumped atomic Bose-Einstein condensate trapped in a ring cavity, corresponding to a superradiant anti-Tavis-Cummings phase transition. In particular, an undamped gapless Goldstone mode is observed in contrast to the experimentally realized lattice supersolid with a gapped roton mode for Dicke superradiance. This zero-energy mode reveals the rigidity of the self-ordered superradiant phase, which spontaneously breaks a continuous translational symmetry. Our work will highlight the significant opportunities for exploring long-lived supersolid matter by utilizing dynamical spin-orbit coupling in controllable optical cavities.

Emergent time crystals from phase-space noncommutative quantum mechanics

It has been argued that the existence of time crystals requires a spontaneous breakdown of the continuous time translation symmetry so to account for the unexpected non-stationary behavior of quantum observables in the ground state. Our point is that such effects do emerge from position (qˆi) and/or momentum (pˆi) noncommutativity, i.e., from [qˆi,qˆj]≠0 and/or [pˆi,pˆj]≠0 (for i≠j). In such a context, a predictive analysis is carried out for the 2-dim noncommutative quantum harmonic oscillator through a procedure supported by the Weyl-Wigner-Groenewold-Moyal framework. This allows for the understanding of how the phase-space noncommutativity drives the amplitude of periodic oscillations identified as time crystals. A natural extension of our analysis also shows how the spontaneous formation of time quasi-crystals can arise.

Line-focus solar concentration 10 times higher than the 2D thermodynamic limit.

Line-focus solar concentrators have traditionally been limited by the 2D concentration limit due to the continuous translational symmetry in these systems. This limit is orders of magnitude lower than the 3D limit, severely limiting the achievable concentration ratio compared to point-focus systems. We propose a design principle for line-focus solar concentrators that bypasses this 2D limit, while maintaining a trough-like configuration and only requiring single-axis external solar tracking. This is achieved by combining the concept of étendue squeezing with the concept of tracking integration. To demonstrate the principle, we present a design example that achieves a simulated average yearly efficiency of 80% at a geometric concentration of 335x under light with a ±9mrad angular distribution and horizontal single-axis external tracking. We also show how the same design principle can achieve a line-focus with 1563x geometric concentration at 90% efficiency if design constraints are relaxed by foregoing tracking-integration and assuming two-axis external solar tracking. This design principle opens up the design space for high-concentration line-focus solar concentrators, and may contribute to a reconsideration of the trade-off between concentration and acceptance angle in such systems.

Observation of a continuous time crystal.

Time crystals are classified as discrete or continuous depending on whether they spontaneously break discrete or continuous time translation symmetry. Although discrete time crystals have been extensively studied in periodically driven systems, the experimental realization of a continuous time crystal is still pending. We report the observation of a limit cycle phase in a continuously pumped dissipative atom-cavity system that is characterized by emergent oscillations in the intracavity photon number. The phase of the oscillation was found to be random for different realizations, and hence, this dynamical many-body state breaks continuous time translation symmetry spontaneously. Furthermore, the observed limit cycles are robust against temporal perturbations and therefore demonstrate the realization of a continuous time crystal.

Experimental verification of ill-defined topologies and energy sinks in electromagnetic continua

It is experimentally verified that nonreciprocal photonic systems with continuous translation symmetry may have an ill-defined topology. The topological classification of such systems is only feasible when the material response is regularized with a spatial-frequency cutoff. We experimentally demonstrate that adjoining a small air layer to the relevant material interface may effectively imitate an idealized spatial cutoff that suppresses the nonreciprocal response for short wavelengths and regularizes the topology. Furthermore, it is experimentally verified that nonreciprocal systems with an ill-defined topology may be used to abruptly halt the energy flow in a unidirectional waveguide due to the violation of the bulk-edge correspondence. In particular, we report the formation of an energy sink that absorbs the incoming electromagnetic waves with a large field enhancement at the singularity.

Intrinsic freedom of dislocation structures and Peierls stress oscillation

When the continuous translation symmetry breaks, a continuous mode splits into two distinct discrete modes with different energies. Based on the fully discrete Peierls model, it is found that stability of such discrete modes for dislocations can be tuned by the stacking fault energy of a slip system. As the stacking fault energy changes continuously, the stable dislocation structure transforms periodically and the Peierls stress varies oscillatorily. Furthermore, at the transformation point, the lattice resistance nearly vanishes and thus the dislocation can almost move freely.

Critical drag as a mechanism for resistivity

A quantum many-body system with a conserved electric charge can have a DC resistivity that is either exactly zero (implying it supports dissipationless current) or nonzero. Exactly zero resistivity is related to conservation laws that prevent the current from degrading. In this paper, we carefully examine the situations in which such a circumstance can occur. We find that exactly zero resistivity requires either continuous translation symmetry, or an internal symmetry that has a certain kind of "mixed anomaly" with the electric charge. (The symmetry could be a generalized global symmetry associated with the emergence of unbreakable loop or higher dimensional excitations.) However, even if one of these is satisfied, we show that there is still a mechanism to get nonzero resistivity, through critical fluctuations that drive the susceptibility of the conserved quantity to infinity; we call this mechanism "critical drag". Critical drag is thus a mechanism for resistivity that, unlike conventional mechanisms, is unrelated to broken symmetries. We furthermore argue that an emergent symmetry that has the appropriate mixed anomaly with electric charge is in fact an inevitable consequence of compressibility in systems with lattice translation symmetry. Critical drag therefore seems to be the only way (other than through irrelevant perturbations breaking the emergent symmetry, that disappear at the renormalization group fixed point) to get nonzero resistivity in such systems. Finally, we present a very simple and concrete model -- the "Quantum Lifshitz Model" -- that illustrates the critical drag mechanism as well as the other considerations of the paper.

Space-time crystalline order of a high-critical-temperature superconductor with intrinsic Josephson junctions

We theoretically demonstrate that the high-critical-temperature (high-Tc) superconductor Bi2Sr2CaCu2O8+x (BSCCO) is a natural candidate for the recently envisioned classical space-time crystal. BSCCO intrinsically forms a stack of Josephson junctions. Under a periodic parametric modulation of the Josephson critical current density, the Josephson currents develop coupled space-time crystalline order, breaking the continuous translational symmetry in both space and time. The modulation frequency and amplitude span a (nonequilibrium) phase diagram for a so-defined spatiotemporal order parameter, which displays rigid pattern formation within a particular region of the phase diagram. Based on our calculations using representative material properties, we propose a laser-modulation experiment to realize the predicted space-time crystalline behavior. Our findings bring new insight into the nature of space-time crystals and, more generally, into nonequilibrium driven condensed matter systems.

Optical forces on a cylinder induced by surface waves and the conservation of the canonical momentum of light.

Based on rigorous derivations using the electromagnetic energy-momentum tensor, we established a generic relationship between the longitudinal optical force (along the surface wave propagating direction) on a cylinder induced by surface waves and the energy flux of each surface mode supported on the interface between air and a lossless substrate possessing continuous translational symmetry along the longitudinal direction. The longitudinal optical force is completely attributed to the canonical momentum of light. Our theory is valid for generic types of surface waves and lays the theoretical foundation for the research and applications of optical manipulations by surface waves.

Computing with non-orientable defects: Nematics, smectics and natural patterns

Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they appear as ‘unphysical’ singularities, with non-integrable energy densities in coarse-grained macroscopic models. We develop a principled approach for enriching coarse-grained theories with enough of the ‘micro-physics’ to obtain thermodynamically consistent, well-set models that allow for the investigations of dynamics and interactions of defects in extended systems. We also develop associated numerical methods that are applicable to computing energy driven behaviors of defects across the amorphous-soft-crystalline materials spectrum. Our methods can handle order parameters that have a head-tail symmetry, i.e. director fields, in systems with a continuous translation symmetry, as in nematic liquid crystals, and in systems where the translation symmetry is broken, as in smectics and convection patterns. We illustrate our methods with explicit computations.

Quantum metamorphism

Crystals form regular and robust structures that under extreme conditions can melt and recrystallize into different arrangements in a process that is called crystal metamorphism. While crystals exist due to the breaking of a continuous translation symmetry in space, it has recently been proposed that discrete crystalline order can also emerge in time and give raise to a novel phase of matter named discrete time crystal (DTC). In this paper, we join these two ideas and propose a model for quantum metamorphism between two DTCs of different periodicity, a 2T and 4T-DTC. In our model the conditions for metamorphism come from the modulation of perturbative terms in the 4T-DTC Hamiltonian that gradually melt its structure and transform it into a 2T-DTC. This process is studied in detail from the viewpoint of manybody physics of periodically driven systems. We also propose a protocol to experimentally observe quantum metamorphism using current quantum technology.

Electron-phonon coupling induced intrinsic Floquet electronic structure

Floquet states are a topic of intense contemporary interest, which is often induced by coherent external oscillating perturbation (e.g., laser, or microwave) which breaks the continuous time translational symmetry of the systems. Usually, electron–phonon coupling modifies the electronic structure of a crystal as a non-coherent perturbation and seems difficult to form Floquet states. Surprisingly, we found that the thermal equilibrium electron–phonon coupling in M(MoS)3 and M(MoSe)3 (where M is a metallic element) exhibits a coherent behavior, and the electronic structure can be described by the Floquet theorem. Such a coherent Floquet state is caused by a selective giant electron–phonon coupling, with thermodynamic phonon oscillation serving as a driving force on the electronic part of the system. The quasi-1D Dirac cone at the Fermi energy has its band gap open and close regularly. Similarly, the electric current will oscillate even under a constant voltage.

General Approach for Reducing Continuous Translational Symmetry Errors in Finite Difference Real-Space Calculations.

We provide a new scheme for representing pseudopotentials on a finite real-space grid, designed to significantly reduce the "egg box" (also known as the "egg carton") effect, i.e., unphysical fluctuations of computed quantities upon real-space translation. Instead of interpolating the electron-ion potential onto the grid, our scheme starts at a reference position and then uses a weighted sum of translation operators to account for the positions of atoms in real space. This results in a nonlocal but banded representation (even for local potentials) which is fully compatible with nonlocal pseudopotential operators. As a demonstration, this scheme is tested in one dimension for three types of potentials: a local pseudopotential, a nonlocal pseudopotential, and a local pseudopotential with self-consistent Hartree and exchange-correlation potentials. This scheme is found to reduce fluctuations of examined quantities by at least three orders of magnitude. The approach requires neither grid adaptation nor pseudopotential modification and can be readily extended to the three-dimensional case.

Supersolid Properties of a Bose-Einstein Condensate in a Ring Resonator.

We investigate the dynamics of a Bose-Einstein condensate interacting with two noninterfering and counterpropagating modes of a ring resonator. Superfluid, supersolid, and dynamic phases are identified experimentally and theoretically. The supersolid phase is obtained for sufficiently equal pump strengths for the two modes. In this regime we observe the emergence of a steady state with crystalline order, which spontaneously breaks the continuous translational symmetry of the system. The supersolidity of this state is demonstrated by the conservation of global phase coherence at the superfluid to supersolid phase transition. Above a critical pump asymmetry the system evolves into a dynamic runaway instability commonly known as collective atomic recoil lasing. We present a phase diagram and characterize the individual phases by comparing theoretical predictions with experimental observations.

Duplex Mikaelian and Duplex Maxwell’s Fish-Eye Lenses

In this paper, we report two new kinds of absolute optical instruments that can make stigmatically images for geometric optics in two dimensional space. One is called the duplex Mikaelian lens, which is made by splicing two half Mikaelian lenses with different periods. The other is exponential conformal transformer of duplex Mikaelian lens with the ratio of different periods of its two half Mikaelian lenses a rational number, which we call duplex Maxwell's fish eye lens. Duplex Mikaelian lenses have continuous translation symmetry with arbitrary real number, while duplex Maxwell's fish eye lenses have continuous rotational symmetry from 0 to 2*Pi. Hence each duplex Maxwell's fish eye lens corresponds to a duplex Mikaelian lens. We further demonstrate the caustic effect of geometric optics in duplex Mikaelian lenses and duplex Maxwell's fish eye lenses. In addition, we investigate the Talbot effect of wave optics in the duplex Mikaelian lens based on numeric calculations. Our findings based on splicing and exponential conformal mapping enlarge the family of absolute optical instruments.

Universal slow plasmons and giant field enhancement in atomically thin quasi-two-dimensional metals

Plasmons depend strongly on dimensionality: while plasmons in three-dimensional systems start with finite energy at wavevector q = 0, plasmons in traditional two-dimensional (2D) electron gas disperse as omega _p sim sqrt q. However, besides graphene, plasmons in real, atomically thin quasi-2D materials were heretofore not well understood. Here we show that the plasmons in real quasi-2D metals are qualitatively different, being virtually dispersionless for wavevectors of typical experimental interest. This stems from a broken continuous translational symmetry which leads to interband screening; so, dispersionless plasmons are a universal intrinsic phenomenon in quasi-2D metals. Moreover, our ab initio calculations reveal that plasmons of monolayer metallic transition metal dichalcogenides are tunable, long lived, able to sustain field intensity enhancement exceeding 107, and localizable in real space (within ~20 nm) with little spreading over practical measurement time. This opens the possibility of tracking plasmon wave packets in real time for novel imaging techniques in atomically thin materials.

Reconciliation of quantum theory and gravitation via redefinition of time in a nondiscrete compressible fluid model of the universe with interactions governed by the Wheeler‐Feynman transactional theory in the quantum-equilibrium theory framework

Recent evidence suggests that the structure and dynamics of planetary scale matter can be described using the wave equation in the form of the Schrödinger equation; thus, suggesting an underlining symmetry across all scales of the universe. Emerging evidences also demonstrate that the complex social-behavior dynamics of animals and other forms of active matter mimic the dynamics of magnetic systems, and are accurately modeled using the framework of quantum theory. However, theoretical frameworks across the different scales of the universe are incompatible, and quantum theory is primarily restricted to the subatomic/atomic scale. This work proposes that the philosophical assumptions concerning the concept time in current theoretical frameworks, as constituting the major barrier in extending quantum theory to all scales of the universe. Time is presumed to be a dimension, in which dynamics occur, with the time dimension interpreted as asymmetric. This interpretation of the concept time contrasts with physics equations, which are time symmetric; and with emerging evidences from neuroscience, which demonstrate that the so-called time dimension along with space dimensions are cognitive constructs. This work proposes a novel theoretical framework, in which the concept time is redefined as a measure of the magnitude of change in location within a nondiscrete compressible fluid universe, which is an enclosed structure. Time and distance are equivalent, as both measure the magnitude of change in location. Matter and vacuum, along with all other constituents of the universe are redefined as demarcated structures, which are manifestations of differential specific energy densities, resulting from compressions and rarefactions. Demarcation of structures denotes a quantum interaction, and the framework of Wheeler‐Feynman transactional theory governs analysis of the dynamics of said demarcated structures. Consequently, the nature and dynamics of demarcated structures at all scales is an emergent equilibrium state of the universe resulting from transactional quantum interactions, which are analyzed using a novel theoretical framework, termed, Quantum-Equilibrium Theory. Per the predictions of Quantum-Equilibrium Theory, this work demonstrates reflection symmetry between the magnetic field and gravitational field, thus unifying the magnetic force and the gravitational force. This work also demonstrates scale symmetry across atomic and galactic structures within the universe. Furthermore, this work demonstrates a continuous translational symmetry between the dynamics of nonactive matter and active matter.