arXiv subjects

Lukas Pausch

Publications and source records attributed to Lukas Pausch.

7 recordsLinked to original sources

arXiv2025

The role of non-Markovian dissipation in quantum phase transitions: tricriticality, spin squeezing, and directional symmetry breaking

Understanding how to control phase transitions in quantum systems is at the forefront of research for the development of new quantum materials and technologies. Here, we study how the coupling of a quantum system to a non-Markovian environment, i.e., an environment with a frequency-dependent spectral density inducing memory effects, can be used to generate and reshape phase transitions and squeezing in matter phases. Focusing on a Lipkin-Meshkov-Glick model, we demonstrate that non-Markovian dissipation can be leveraged to engineer tricriticality via the fusion of $2^{\mathrm{nd}}$-order and $1^{\mathrm{st}}$-order critical points. We identify phases that arise from different ways of breaking the single weak symmetry of our model, which led us to introduce the concept of \textit{directional spontaneous symmetry breaking} (DSSB) as a general framework to understand this phenomenon. We show that signatures of DSSB can be seen in the emergence of spin squeezing along different directions, and that the latter is controllable via non-Markovian effects, opening up possibilities for applications in quantum metrology. Finally, we propose an experimental implementation of our non-Markovian model in cavity QED. Our work features non-Markovianity as a resource for controlling phase transitions in general systems, and highlights shortcomings of the Markovian limit in this context.

quant-ph↗

arXiv2025

How to seed ergodic dynamics of interacting bosons under conditions of many-body quantum chaos

We demonstrate how the initial state of ultracold atoms in an optical lattice controls the emergence of ergodic dynamics as the underlying spectral structure is tuned into the quantum chaotic regime. Distinct initial states' chaos threshold values in terms of tunneling as compared to interaction strength are identified, as well as dynamical signatures of the chaos transition, on the level of experimentally accessible observables and time scales.

quant-ph↗

arXiv2024

Dissipative phase transition: from qubits to qudits

We investigate the fate of dissipative phase transitions in quantum many-body systems when the individual constituents are qudits ($d$-level systems) instead of qubits. As an example system, we employ a permutation-invariant $XY$ model of $N$ infinite-range interacting $d$-level spins undergoing individual and collective dissipation. In the mean-field limit, we identify a dissipative phase transition, whose critical point is independent of $d$ after a suitable rescaling of parameters. When the decay rates between all adjacent levels are identical and $d\geq 4$, the critical point expands, in terms of the ratio between dissipation and interaction strengths, to a critical region in which two phases coexist and which increases as $d$ grows. In addition, a larger $d$ leads to a more pronounced change in spin expectation values at the critical point. Numerical investigations for finite $N$ reveal symmetry breaking signatures in the Liouvillian spectrum at the phase transition. The phase transition is furthermore marked by maximum entanglement negativity and a significant purity change of the steady state, which become more pronounced as $d$ increases. Considering qudits instead of qubits thus opens new perspectives on accessing rich phase diagrams in open many-body systems.

quant-ph↗

arXiv2022

Many-body interference at the onset of chaos

We unveil the signature of many-body interference across dynamical regimes of the Bose-Hubbard model. Increasing the particles' indistinguishability enhances the temporal fluctuations of few-body observables, with a dramatic amplification at the onset of quantum chaos. By resolving the exchange symmetries of partially distinguishable particles, we explain this amplification as the fingerprint of the initial state's coherences in the eigenbasis.

quant-ph↗

arXiv2022

Optimal route to quantum chaos in the Bose-Hubbard model

The dependence of the chaotic phase of the Bose-Hubbard Hamiltonian on particle number $N$, system size $L$ and particle density is investigated in terms of spectral and eigenstate features. We analyze the development of the chaotic phase as the limit of infinite Hilbert space dimension is approached along different directions, and show that the fastest route to chaos is the path at fixed density $n \lesssim 1$. The limit $N \to \infty$ at constant $L$ leads to a slower convergence of the chaotic phase towards the random matrix theory benchmarks. In this case, from the distribution of the eigenstate generalized fractal dimensions, the ergodic phase becomes more distinguishable from random matrix theory for larger $N$, in a similar way as along trajectories at fixed density.

quant-ph↗

arXiv2021

Chaos in the Bose-Hubbard model and random two-body Hamiltonians

We investigate the chaotic phase of the Bose-Hubbard model [L. Pausch et al, Phys. Rev. Lett. 126, 150601 (2021)] in relation to the bosonic embedded random matrix ensemble, which mirrors the dominant few-body nature of many-particle interactions, and hence the Fock space sparsity of quantum many-body systems. The energy dependence of the chaotic regime is well described by the bosonic embedded ensemble, which also reproduces the Bose-Hubbard chaotic eigenvector features, quantified by the expectation value and eigenstate-to-eigenstate fluctuations of fractal dimensions. Despite this agreement, in terms of the fractal dimension distribution, these two models depart from each other and from the Gaussian orthogonal ensemble as Hilbert space grows. These results provide further evidence of a way to discriminate among different many-body Hamiltonians in the chaotic regime.

quant-ph↗

arXiv2020

Chaos and ergodicity across the energy spectrum of interacting bosons

We identify the chaotic phase of the Bose-Hubbard Hamiltonian by the energy-resolved correlation between spectral features and structural changes of the associated eigenstates as exposed by their generalized fractal dimensions. The eigenvectors are shown to become ergodic in the thermodynamic limit, in the configuration space Fock basis, in which random matrix theory offers a remarkable description of their typical structure. The distributions of the generalized fractal dimensions, however, are ever more distinguishable from random matrix theory as the Hilbert space dimension grows.

cond-mat.quant-gas↗