Non-equilibrium scale invariance and shortcuts to adiabaticity in a one-dimensional Bose gas

Rohringer, Wolfgang; Fischer, Dominik; Steiner, Florian; Mazets, I. E.; Schmiedmayer, Jörg; Trupke, Michael

doi:10.1038/srep09820

Cited by 65 publications

(70 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the linear increase in system energy is ubiquitously observed, also in experiments in the spatial continuum [34]. This effect is captured by the continuum heating term in Eq.…”

Section: A Master Equation In the Luttinger Descriptionmentioning

confidence: 85%

Nonequilibrium universality in the heating dynamics of interacting Luttinger liquids

Buchhold

Diehl

2015

Phys. Rev. A

View full text Add to dashboard Cite

We establish a new non-equilibrium scaling regime in the short time evolution of one-dimensional interacting open quantum systems subject to a generic heating mechanism. This dynamical regime is characterized by uncompensated phonon production and a super-diffusive, universal scaling of quasiparticle lifetimes with momentum ∼ q −5/3 , distinct from finite and zero temperature cases. It is separated from a high momentum regime by a time dependent scale fading out as q0(t) ∼ t −4/5 . In the latter region we observe thermalization to an effective time-dependent equilibrium with linearly increasing temperature. By mapping out the dynamical phase diagram and computing the dynamical structure factor within an open system Keldysh functional integral approach, we show how these predictions can be explored in cold atom experiments by means of Bragg spectroscopy.

show abstract

“…However, the linear increase in system energy is ubiquitously observed, also in experiments in the spatial continuum [34]. This effect is captured by the continuum heating term in Eq.…”

Section: A Master Equation In the Luttinger Descriptionmentioning

confidence: 85%

Nonequilibrium universality in the heating dynamics of interacting Luttinger liquids

Buchhold

Diehl

2015

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…Concerning the relevance of the interacting Luttinger model, before closing the section, we would like to mention that only recently pioneering experiments in ultra-cold gases both in and out of equilibrium explored the transient and prethermalization dynamics of systems [16][17][18][19][20][21][22][23][24][25][26][68][69][70] effectively described by a quadratic Luttinger model, the bosonic theory of the Hamiltonian in Eq. (2.2).…”

Section: Interacting Luttinger Liquidmentioning

confidence: 99%

“…In particular, in Refs. [16][17][18]24] prethermal states in the relative phase of a suddenly split condensate have been identified that have been stable on the experimentally accessible time scales. For the latter experiments, the cubic nonlinearity studied in the present work constitutes the leading order correction to the quadratic theory in a gradient expansion.…”

Section: Interacting Luttinger Liquidmentioning

confidence: 99%

Prethermalization and thermalization of a quenched interacting Luttinger liquid

2016

View full text Add to dashboard Cite

We study the relaxation dynamics of interacting, one-dimensional fermions with band curvature after a weak quench in the interaction parameter at zero temperature. Our model lies within the class of interacting Luttinger Liquids, where the harmonic Luttinger theory is extended by a weak integrability breaking phonon scattering term. In order to solve for the non-equilibrium time evolution, we use quantum kinetic equations exploiting the resonant but subleading character of the phonon interaction term. The interplay between phonon scattering and the quadratic Luttinger theory leads to the emergence of three distinct spatio-temporal regimes for the fermionic real-space correlation function. It features the crossover from a prequench to a prethermal state, finally evolving towards a thermal state on increasing length and time scales. The characteristic algebraically decaying real-space correlations in the prethermalized regime become modulated by an amplitude, which is decaying in time according to a stretched-exponential as an effect of the interactions. The asymptotic thermalization dynamics is governed by energy transport over large distances from the thermalized to the non-thermalized regions via macroscopic, dynamical slow modes. This is revealed in an algebraic decay of the system's effective temperature. The numerical value of the associated exponent agrees with the dynamical critical exponent of the Kardar-Parisi-Zhang universality class. We also discuss a criterion for the applicability of this theory away from the integrable limit of non-interacting fermions.

show abstract

“…[40,41]); (iii) Application of imperfect external drivings which do not allow for an exact adiabatic transfer, but close enough for most practical purposes (e.g. [42][43][44]). …”

Section: Introductionmentioning

confidence: 99%

Cost of counterdiabatic driving and work output

et al. 2016

View full text Add to dashboard Cite

Unitary processes allow for the transfer of work to and from Hamiltonian systems. However, to achieve non-zero power for the practical extraction of work, these processes must be performed within a finite-time, which inevitably induces excitations in the system. We show that depending on the time-scale of the process and the physical realization of the external driving employed, the use of counterdiabatic quantum driving to extract more work is not always effective. We also show that by virtue of the two-time energy measurement definition of quantum work, the cost of counterdiabatic driving can be significantly reduced by selecting a restricted form of the driving Hamiltonian that depends on the outcome of the first energy measurement. Lastly, we introduce a measure, the exigency, that quantifies the need for an external driving to preserve quantum adiabaticity which does not require knowledge of the explicit form of the counterdiabatic drivings, and can thus always be computed. We apply our analysis to systems ranging from a two-level Landau-Zener problem to many-body problems, namely the quantum Ising and Lipkin-Meshkov-Glick models.

show abstract

Non-equilibrium scale invariance and shortcuts to adiabaticity in a one-dimensional Bose gas

Cited by 65 publications

References 50 publications

Nonequilibrium universality in the heating dynamics of interacting Luttinger liquids

Nonequilibrium universality in the heating dynamics of interacting Luttinger liquids

Prethermalization and thermalization of a quenched interacting Luttinger liquid

Cost of counterdiabatic driving and work output

Contact Info

Product

Resources

About