arXiv subjects

Krzysztof Sacha

Publications and source records attributed to Krzysztof Sacha.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Boomerang Effect in Time-Crystalline Structures

The quantum boomerang effect (QBE) is a unique dynamical signature of Anderson localization, characterized by a launched wavepacket that initially drifts but ultimately returns to its initial position due to fundamental quantum interference. In this work, we theoretically establish and quantitatively characterize the QBE in a time-crystalline structure using a periodically driven quantum particle in a one-dimensional potential well. By constructing maximally localized Floquet-Wannier states and introducing temporal disorder, we rigorously map the continuous Floquet dynamics onto a discrete disordered tight-binding lattice. By positioning a detector at a fixed spatial coordinate, we monitor the temporal evolution of the wavepacket, to extract the mean temporal center of mass of the probability density in a time-crystalline structure. This mean temporal center of mass exhibits an initial ballistic expansion, followed by a pronounced U-turn, and ultimately returns to its initial temporal position after long-time evolution. These results confirm the existence of the complete QBE in the time domain. They also demonstrate that non-trivial dynamics can be explored within time-crystalline systems, even though these structures already possess an inherent temporal periodicity.

quant-ph↗

arXiv2026

Engineering interactions shape in resonantly driven bosonic gas

In systems with fast periodic driving, there are special subsets of (resonant) states, which behavior can be described with effective, time-independent Hamiltonian in a rotating reference frame. Here, we show that experimentally feasible system of ultracold bosonic atoms on a ring with rapidly oscillating scattering length can be used to simulate time-independent two-component atomic mixture with exotic, long-range interactions.

cond-mat.quant-gas↗

arXiv2025

Aspects of quantum geometry in photonic time crystals

We develop a geometric description of quantum light in photonic time crystals on the SU(1,1) coherent-state manifold. In a projective picture, the evolution of each mode appears as a Möbius isometry on the Poincaré disk, where topologies of trajectories distinguish stable, unstable, and critical regimes. The geometric phase is related to the hyperbolic area enclosed by cyclic paths in the complex projective Hilbert space. This framework offers an intuitive view of stability and topology in quantum photonic time crystals.

physics.optics↗

arXiv2025

Time-tronics: from temporal printed circuit board to quantum computer

Time crystalline structures can be created in periodically driven systems. They are temporal lattices which can reveal different condensed matter behaviours ranging from Anderson localization in time to temporal analogues of many-body localization or topological insulators. However, the potential practical applications of time crystalline structures have yet to be explored. Here, we pave the way for time-tronics where temporal lattices are like printed circuit boards for realization of a broad range of quantum devices. The elements of these devices can correspond to structures of dimensions higher than three and can be arbitrarily connected and reconfigured at any moment. Moreover, our approach allows for the construction of a quantum computer, enabling quantum gate operations for all possible pairs of qubits. Our findings indicate that the limitations faced in building devices using conventional spatial crystals can be overcome by adopting crystalline structures in time.

cond-mat.quant-gas↗

arXiv2025

Towards Timetronics with Photonic Systems

Periodic driving of particles can create crystalline structures in their dynamics. Such systems can be used to study solid-state physics phenomena in the time domain. In addition, it is possible to realize photonic time crystals and to engineer the wave-number band structure of optical devices by periodic temporal modulation of the properties of light-propagating media. Here we introduce a versatile approach which uses traveling wave resonators to emulate various condensed matter phases in the time dimension. This is achieved by utilizing temporal modulation of the permittivity and the shape of small segments of the resonators. The required frequency and depth of the modulation are experimentally achievable which opens a pathway for the practical realisation of crystalline structures in time in microwave and in optical systems.

physics.optics↗

arXiv2025

Anderson Localization in Photonic Time Crystals

Solutions of the wave equations for time-independent disordered media can exhibit Anderson localization where instead of wave propagation we observe their localization around different points in space. Photonic time crystals are spatially homogeneous media in which the refractive index changes periodically in time, leading to the formation of bands in the wave number domain. By analogy to Anderson localization in space, one might expect that the presence of temporal disorder in photonic time crystals would lead to Anderson localization in the time domain. Here, we show that indeed periodic modulations of the refractive index with the addition of temporal disorder lead to Anderson localization in time, where an electromagnetic field can emerge from the temporally modulated medium at a certain moment in time and then decay exponentially over time. Thus, we are dealing with a situation where, in a fluctuating three-dimensional medium, the birth and death of waves can occur, and the mechanism of this phenomenon corresponds to Anderson localization.

physics.optics↗

arXiv2025

Discrete Time Crystal Phase as a Resource for Quantum Enhanced Sensing

Discrete time crystals are a special phase of matter in which time translational symmetry is broken through a periodic driving pulse. Here, we first propose and characterize an effective mechanism to generate a stable discrete time crystal phase in a disorder-free many-body system with indefinite persistent oscillations even in finite-size systems. Then we explore the sensing capability of this system to measure the spin exchange coupling. The results show strong quantum-enhanced sensitivity throughout the time crystal phase. As the spin exchange coupling varies, the system goes through a sharp phase transition and enters a non-time crystal phase in which the performance of the probe considerably decreases. We characterize this phase transition as a second-order type and determine its critical properties through a comprehensive finite-size scaling analysis. The performance is independent of the initial states and may even benefit from imperfections in the driving pulse. A simple set of projective measurements can capture the quantum-enhanced sensitivity.

quant-ph↗

arXiv2025

Formation of Complex Discrete Time Crystals with Ultracold Atoms

We study discrete time crystal formation in a system driven periodically by an oscillating atomic mirror, consisting of two distinct ultracold atomic clouds in the presence of a gravitational field. The intra-species interactions are weak and attractive, while the inter-species interactions are infinitely strong and repulsive. The clouds are arranged in a one-dimensional stack, where the bottom cloud bounces on an oscillating atomic mirror, which effectively acts as a driving force for the upper cloud due to the infinite inter-species repulsion. Using a Jastrow-like variational ansatz for the many-body wavefunction, we show that sufficiently strong attractive intra-species interactions drive each subsystem to spontaneously break discrete time translation symmetry, resulting in the formation of a complex discrete time crystal evolving with a period different than the driving period. Since the bottom cloud serves as the effective periodic driving for the upper cloud, this leads to a cascade of spontaneous symmetry breaking. With increasing intra-species interactions, we first observe a pronounced effect of spontaneous time translation symmetry breaking in the upper cloud, followed by a similar effect in the lower atomic cloud.

cond-mat.quant-gas↗

arXiv2025

Quantum Measurements of Time: A reply to criticisms

In [arXiv:2409.00161v1 (2024)] Cavendish et al. raise three criticisms against our time of arrival proposal [L. Maccone and K. Sacha, Phys. Rev. Lett. 124, 110402 (2020)]. Here we show that all three criticisms are without merit. One of them is founded on a logical mistake.

quant-ph↗

arXiv2024

Temporal localization of optical waves supported by a copropagating quasiperiodic structure

Research on time crystals concerns the spontaneous breaking of translational symmetry in time, as well as the realization of phenomena and phases known from solid-state physics in the time domain. Periodically driven systems of massive particles are widely used in these studies. In the present work, we consider a photonic system and demonstrate that stable nonlinear propagation of a strong optical wave in a fiber leads to the establishment of quasi-periodic oscillations in the electromagnetic field intensity. A second, weaker signal optical wave propagating in the fiber senses these oscillations and, as a result, undergoes exponential localization in time. This is a temporal analogue of Aubry-Andre localization. If an optical detector is placed at a certain position in the fiber, the temporal localization of the probe wave will be observed in the form of the signal which emerges and then decays as a function of time.

physics.optics↗

arXiv2024

Non-Hermitian Discrete Time Crystals

Discrete time crystals (DTC) exhibit a special non-equilibrium phase of matter in periodically driven many-body systems with spontaneous breaking of time translational symmetry. The presence of decoherence generally enhances thermalization and destroys the coherence required for the existence of DTC. In this letter, we devise a mechanism for establishing a stable DTC with period-doubling oscillations in an open quantum system that is governed by a properly tailored non-Hermitian Hamiltonian. We find a specific class of non-reciprocal couplings in our non-Hermitian dynamics which prevents thermalization through eigenstate ordering. Such choice of non-Hermitian dynamics, significantly enhances the stability of the DTC against imperfect pulses. Through a comprehensive analysis, we determine the phase diagram of the system in terms of pulse imperfection.

quant-ph↗

arXiv2024

Topologically protected quantized changes of the distance between atoms

Thouless pumping enables the transport of particles in a one-dimensional periodic potential if the potential is slowly and periodically modulated in time. The change in the position of particles after each modulation period is quantized and depends solely on the topology of the pump cycle, making it robust against perturbations. Here, we demonstrate that Thouless pumping also allows for the realization of topologically protected quantized changes of the distance between atoms if the atomic s-wave scattering length is properly modulated in time.

cond-mat.quant-gas↗

arXiv2023

Discrete Time Crystals with Absolute Stability

We show that interacting bosons on a ring which are driven periodically by a rotating potential can support discrete time crystals whose absolute stability can be proven. The absolute stability is demonstrated by an exact mapping of discrete time crystal states to low-lying eigenstates of a time-independent model that reveals spontaneous breaking of space translation symmetry. The mapping ensures that there are no residual time-dependent terms that could lead to heating of the system and destruction of discrete time crystals. We also analyze periodically kicked bosons where the mapping is approximate only and cannot guarantee the absolute stability of discrete time crystals. Besides illustrating potential sources of instability, the kicked bosons model demonstrates a rich field for investigating the interplay between different time and space symmetry breaking, as well as the stability of time crystal behavior in contact with a thermal reservoir.

cond-mat.quant-gas↗

arXiv2023

Eight-dimensional topological systems simulated using time-space crystalline structures

We demonstrate the possibility of using time-space crystalline structures to simulate eight-dimensional systems based on only two physical dimensions. A suitable choice of system parameters allows us to obtain a gapped energy spectrum, making topological effects become relevant. The nontrivial topology of the system is evinced by considering the adiabatic state pumping along temporal and spatial crystalline directions. Analysis of the system is facilitated by rewriting the system Hamiltonian in a tight-binding form, thereby putting space, time, and the additional synthetic dimensions on an equal footing.

cond-mat.quant-gas↗

arXiv2023

Classical Phase Space Crystals in an Open Environment

It was recently discovered that a crystalline many-body state can exist in the phase space of a closed dynamical system. A phase space crystal can be an anomalous Chern insulator that supports chiral topological transport without breaking physical time-reversal symmetry [L. Guo et al., Phys. Rev. B 105, 094301 (2022)]. In this work, we further study the effects of an open dissipative environment with thermal noise and identify the existence condition of classical phase space crystals in realistic scenarios. By defining a crystal order parameter, we plot the phase diagram in the parameter space of dissipation rate, interaction, and temperature. Our present work paves the way to realize phase space crystals and explore anomalous chiral transport in experiments.

cond-mat.quant-gas↗

arXiv2023

When does a particle arrive?

We compare the proposals that have appeared in the literature to describe a measurement of the time of arrival of a quantum particle at a detector. We show that there are multiple regimes where different proposals give inequivalent, experimentally discriminable, predictions. This analysis paves the way for future experimental tests.

quant-ph↗

arXiv2022

Basis for time crystal phenomena in ultra-cold atoms bouncing on an oscillating mirror

We consider classical dynamics of a 1D system of $N$ particles bouncing on an oscillating mirror in the presence of gravitational field. The particles behave like hard balls and they are resonantly driven by the mirror. We identify the manifolds the particles move on and derive the effective secular Hamiltonian for resonant motion of the particles. Proper choice of time periodic oscillations of the mirror allows for engineering of the effective behaviour of the particles. In particular, the system can behave like a $N$-dimensional fictitious particle moving in an $N$-dimensional crystalline structure. Our classical analysis constitutes a basis for quantum research of novel time crystal phenomena in ultra-cold atoms bouncing on an oscillating atom mirror.

cond-mat.quant-gas↗

arXiv2022

Topological Molecules and Topological Localization of a Rydberg Electron on a Classical Orbit

It is common knowledge that atoms can form molecules if they attract each other. Here, we show that it is possible to create molecules where bound states of the atoms are not the result of attractive interactions but have the topological origin. That is, the bound states of the atoms correspond to the topologically protected edge states of a topological model. Such topological molecules can be realized if the interaction strength between ultra-cold atoms is properly modulated in time. A similar mechanism allows one to realize topologically protected localization of an electron on a classical orbit if a Rydberg atom is perturbed by a properly modulated microwave field.

quant-ph↗