arXiv subjects

Samuel Alperin

Publications and source records attributed to Samuel Alperin.

7 recordsLinked to original sources

arXiv2026

Exact Self-Imaging with Arbitrary Revival Spacings

Self-imaging represents a core hallmark of paraxial wave evolution; yet, across its many realizations and generalizations over the past two centuries, the uniformity of recurrence planes along the propagation axis has been considered fundamental. Here we reformulate the general phenomenon of self-imaging within the natural framework of canonical phase-space geometry, revealing a hidden canonical coordinate in which all exact self-imaging is indeed uniform, but which need not correspond to the physical propagation axis. This leads to a general law of self-imaging, in which the spacing of the physical recurrence planes can be prescribed through the choice of initial transverse phase structure. Using a single programmable spatial light modulator, we demonstrate the construction of Talbot carpets characterized by recurrence spacings that accelerate and decelerate along the propagation axis, as well as those that follow polynomial, exponential, and sinusoidal axial trajectories. These results reveal a hidden geometric freedom in paraxial wave propagation: exact self-imaging is rigid in canonical coordinates, but freely programmable in physical space, allowing for qualitatively new forms of optical recurrence.

physics.optics↗

arXiv2025

Universal Limits on Quantum Correlations

Quantum correlations are the singular, defining resource of quantum information science and metrology, forming the basis of every operational advantage that quantum systems hold over classical ones. Yet exact bounds on these correlations-such as the Lieb-Robinson bound on entanglement propagation and the Heisenberg limit on metrological precision-are known only in special cases and have long appeared to arise from unrelated mechanisms. Here we show that these limits share a common geometric origin. We identify a positivity invariant of the block correlation matrix, denoted $\chi$, that quantifies how far a bipartite state lies from the positivity boundary of quantum state space. For any system with a specified observable algebra and parameter-encoding map, every correlation measure determined solely by the positive correlation matrix obeys a $\chi$-dependent inequality. For systems with simple symmetry structures these inequalities take closed analytic form, reproducing the structure of the Heisenberg and Cram\'er-Rao limits and producing new results, including an exact entanglement floor and a universal Fisher-information ceiling even in all-to-all connected quantum networks. We thus demonstrate that positive geometry provides a unified framework for the attainable strength of quantum correlations, linking entanglement, metrological sensitivity, and dynamical causal structure through a single invariant.

quant-ph↗

arXiv2025

A No-Go Theorem for Shaping Quantum Resources

The ability to engineer non-Gaussian quantum resources underlies quantum technologies from communication and metrology to universal computation. However, while a number of canonical works have set no-go limits for attaining such resources from Gaussian operations, it is widely assumed that such resources can be tuned freely by non-Gaussian Hamiltonian dynamics. Here we prove a general no-go theorem for such resource shaping: no smooth Hamiltonian dynamics can modify higher-order statistical moments of a continuous-variable state without simultaneously changing its mean and covariance. This analytic constraint implies a rigidity theorem for Hamiltonian quantum control-only quadratic (symplectic) generators preserve the Gaussian moment hierarchy, while every non-quadratic term necessarily couples the Gaussian and non-Gaussian sectors. The theorem identifies the symplectic algebra as the unique invariant subalgebra whose differential representations terminate at finite (second) order within the otherwise infinite Hamiltonian algebra. It thereby defines the analytic boundary between classically simulable Gaussian dynamics and the fully universal non-Gaussian regime-the continuous-variable analogue of the Gottesman-Knill frontier.

quant-ph↗

arXiv2025

Non-Hermitian Realization of Quantum Dynamics on Embedded Manifolds

We show that the Floquet Hamiltonian of a quantum particle driven by a general time-periodic imaginary potential is exactly equivalent, at stroboscopic times, to the Hamiltonian of a free particle constrained to a curved Riemannian manifold with fixed embedding. We illustrate the construction for a sinusoidal drive and for the torus of revolution, and outline how the framework can guide experimental design of curved-space quantum dynamics. Our results unify non-Hermitian Floquet physics with spectral geometry and provide a general recipe for engineering quantum dynamics on embedded manifolds.

quant-ph↗

arXiv2025

Real-Time Instantons in Complex-Driven Qubits

We consider the dynamics of the quantum Rabi model driven parametrically by a periodic modulation of a complex coupling. We show both analytically and numerically that instead of Rabi oscillations, this nonunitary coherent driving leads to a unidirectional instanton solution which mediates the rapid and deterministic one-way tunneling of any initial coherent state to the ground state, making the ground state a strong attractor in the quantum dynamics of the qubit. The timescale of this tunneling is shown to be inversely proportional to the effective resonant coupling, allowing for exceptionally fast, deterministic, and high-fidelity qubit reset through a purely coherent, PT-symmetric drive--without coupling to external dissipative baths, lossy resonators, or employing measurement-based feedback. Finally, we show how the drive can be engineered to place the strong attractor at any arbitrary point on the Bloch sphere.

quant-ph↗

arXiv2025

The Quantum Foucault Modes

The driven quantum harmonic oscillator is fundamental to a number of important physical systems. Here, we consider the quantum harmonic oscillator under non-Hermitian, PT-symmetric driving, showing that the resulting set of Wigner-space trajectories of an initial coherent state is identical to the set of real-space trajectories of the classical Foucault pendulum. Remarkably, in the case mapped from the trivial 1D pendulum, the corresponding quantum dynamics are those of an oscillator with periodically evolving momentum but fixed position, a novel type of dynamics which are forbidden in classical systems.

quant-ph↗

arXiv2025

Counterflow leads to roton spectra in locally interacting superfluids

The dynamics of strongly interacting quantum fluids such as Helium II are fundamentally distinct from those of dilute, contact-interacting atomic Bose-Einstein condensates. Most dramatically, superfluids with finite-range interactions can support excitations with a roton-like dispersion, exhibiting a minimum at finite wavenumber. Here we introduce a mechanism through which roton spectra can emerge in superfluids without any nonlocal interactions, instead resulting from the collective excitations of two counterflowing, zero-range interacting condensates. As our mechanism relies only on the nonlinear dynamics of classical fields, this work opens the door to the realization of roton dynamics in the broad class of physical systems governed by coupled nonlinear-Schr\"odinger equations.

cond-mat.quant-gas↗