Publications

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Optimizing Floquet engineering for non-equilibrium steady states with gradient-based methods

Alberto Castro, Shunsuke A. Sato

SciPost Phys. 15, 029 (2023) · published 26 July 2023 | · pdf

Non-equilibrium steady states are created when a periodically driven quantum system is also incoherently interacting with an environment - as it is the case in most realistic situations. The notion of Floquet engineering refers to the manipulation of the properties of systems under periodic perturbations. Although it more frequently refers to the coherent states of isolated systems (or to the transient phase for states that are weakly coupled to the environment), it may sometimes be of more interest to consider the final steady states that are reached after decoherence and dissipation take place. In this work, we demonstrate how those final states can be optimally tuned with respect to a given predefined metric, such as for example the maximization of the temporal average value of some observable, by using multicolor periodic perturbations. We show a computational framework that can be used for that purpose, and exemplify the concept using a simple model for the nitrogen-vacancy center in diamond: the goal in this case is to find the driving periodic magnetic field that maximizes a time-averaged spin component. We show that, for example, this technique permits to prepare states whose spin values are forbidden in thermal equilibrium at any temperature.

1 citation
Topological states between inversion symmetric atomic insulators

Ana Silva, Jasper van Wezel

SciPost Phys. 10, 137 (2021) · published 8 June 2021 | · pdf

One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary correspondence has been well-tested for strong topological invariants, and forms the basis for all proposed technological applications of topology. Here, we report that a group of weak topological invariants, which depend only on the symmetries of the atomic lattice, also induces a particular type of bulk-boundary correspondence. It predicts the presence or absence of states localised at the interface between two inversion-symmetric band insulators with trivial values for their strong invariants, based on the space group representation of the bands on either side of the junction. We show that this corresponds with symmetry-based classifications of topological materials. The interface modes are protected by the combination of band topology and symmetry of the interface, and may be used for topological transport and signal manipulation in heterojunction-based devices.

1 citation
Asymmetric power dissipation in electronic transport through a quantum point contact

Carmen Blaas-Anselmi, Félix Helluin, Rodolfo A. Jalabert, Guillaume Weick, Dietmar Weinmann

SciPost Phys. 12, 105 (2022) · published 25 March 2022 | · pdf

We investigate the power dissipated by an electronic current flowing through a quantum point contact in a two-dimensional electron gas. Based on the Landauer-B\"uttiker approach to quantum transport, we evaluate the power that is dissipated on the two sides of the constriction as a function of the Fermi energy, temperature, and applied voltage. We demonstrate that an asymmetry appears in the dissipation, which is most pronounced when the quantum point contact is tuned to a conductance step where the transmission strongly depends on energy. At low temperatures, the asymmetry is enhanced when the temperature increases. An estimation for the position of the maximum dissipation is provided.

1 citation
Exceptional points and pseudo-Hermiticity in real potential scattering

Farhang Loran, Ali Mostafazadeh

SciPost Phys. 12, 109 (2022) · published 28 March 2022 | · pdf

We employ a recently-developed transfer-matrix formulation of scattering theory in two dimensions to study a class of scattering setups modeled by real potentials. The transfer matrix for these potentials is related to the time-evolution operator for an associated pseudo-Hermitian Hamiltonian operator $\widehat{\boldsymbol{H}}$ which develops an exceptional point for a discrete set of incident wavenumbers. We use the spectral properties of this operator to determine the transfer matrix of these potentials and solve their scattering problem. We apply our general results to explore the scattering of waves by a waveguide of finite length in two dimensions, where the source of the incident wave and the detectors measuring the scattered wave are positioned at spatial infinities while the interior of the waveguide, which is filled with an inactive material, forms a finite rectangular region of the space. The study of this model allows us to elucidate the physical meaning and implications of the presence of the real and complex eigenvalues of $\widehat{\boldsymbol{H}}$ and its exceptional points. Our results reveal the relevance of the concepts of pseudo-Hermitian operator and exceptional point in the standard quantum mechanics of closed systems where the potentials are required to be real.

1 citation
Puzzles and pitfalls involving Haar-typicality in holography

Ning Bao, Aidan Chatwin-Davies

SciPost Phys. 4, 033 (2018) · published 19 June 2018 | · pdf

Holographic states that have a well-defined geometric dual in AdS/CFT are not faithfully represented by Haar-typical states in finite-dimensional models. As such, trying to apply principles and lessons from Haar-random ensembles of states to holographic states can lead to apparent puzzles and contradictions. We point out a handful of these pitfalls.

1 citation
Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity

Victoria L. Martin, Andrew Svesko

SciPost Phys. 9, 039 (2020) · published 14 September 2020 | · pdf

In this note we compute the 1-loop partition function of spin-$s$ fields on Euclidean de Sitter space $S^{2n+1}$ using the quasinormal mode method. Instead of computing the quasinormal mode frequencies from scratch, we use the analytic continuation prescription $L_{\text{AdS}}\to iL_{\text{dS}}$, appearing in the dS/CFT correspondence, and Wick rotate the normal mode frequencies of fields on thermal $\text{AdS}_{2n+1}$ into the quasinormal mode frequencies of fields on de Sitter space. We compare the quasinormal mode and heat kernel methods of calculating 1-loop determinants, finding exact agreement, and furthermore explicitly relate these methods via a sum over the conformal dimension. We discuss how the Wick rotation of normal modes on thermal $\text{AdS}_{2n+1}$ can be generalized to calculating 1-loop partition functions on the thermal spherical quotients $S^{2n+1}/\mathbb{Z}_{p}$. We further show that the quasinormal mode frequencies encode the group theoretic structure of the spherical spacetimes in question, analogous to the recent analysis made for thermal AdS in (1910.07607) and (1910.11913).

1 citation
Super-diffusion and crossover from diffusive to anomalous transport in a one-dimensional system

Anupam Kundu

SciPost Phys. 15, 038 (2023) · published 31 July 2023 | · pdf

We study transport in a one-dimensional lattice system with two conserved quantities - "volume" and energy. Considering a slowly evolving local equilibrium state that is slightly deviated from an underlying global equilibrium, we estimate the correction to the local equilibrium distribution. This correction arises mainly through the space-time correlations of some local currents. In the continuum limit, we show that the local equilibrium distribution along with the correction yields drift-diffusion equation for the "volume" and super-diffusion equation for the energy in the linear response regime as macroscopic hydrodynamics as one would obtain from non-linear fluctuating hydrodynamic theory. We find explicit expression of the super-diffusion equation. Further, we find diffusive correction to the super-diffusive evolution. Such a correction allows us to study a crossover from diffusive to anomalous transport. We demonstrate this crossover numerically through the spreading of an initially localized heat pulse in equilibrium as well as through the system size scaling of the stationary current in non-equilibrium steady state.

1 citation
Anomalies of generalized symmetries from solitonic defects

Lakshya Bhardwaj, Mathew Bullimore, Andrea E. V. Ferrari, Sakura Schäfer-Nameki

SciPost Phys. 16, 087 (2024) · published 26 March 2024 | · pdf

We propose the general idea that 't Hooft anomalies of generalized global symmetries can be understood in terms of the properties of solitonic defects, which generically are non-topological defects. The defining property of such defects is that they act as sources for background fields of generalized symmetries. 't Hooft anomalies arise when solitonic defects are charged under these generalized symmetries. We illustrate this idea for several kinds of anomalies in various spacetime dimensions. A systematic exploration is performed in 3d for 0-form, 1-form, and 2-group symmetries, whose 't Hooft anomalies are related to two special types of solitonic defects, namely vortex line defects and monopole operators. This analysis is supplemented with detailed computations of such anomalies in a large class of 3d gauge theories. Central to this computation is the determination of the gauge and 0-form charges of a variety of monopole operators: these involve standard gauge monopole operators, but also fractional gauge monopole operators, as well as monopole operators for 0-form symmetries. The charges of these monopole operators mainly receive contributions from Chern-Simons terms and fermions in the matter content. Along the way, we interpret the vanishing of the global gauge and ABJ anomalies, which are anomalies not captured by local anomaly polynomials, as the requirement that gauge monopole operators and mixed monopole operators for 0-form and gauge symmetries have non-fractional integer charges.

1 citation
Quasi-equilibrium polariton condensates in the non-linear regime and beyond

Ned Goodman, Brendan C. Mulkerin, Jesper Levinsen, Meera M. Parish

SciPost Phys. 15, 116 (2023) · published 26 September 2023 | · pdf

We investigate the many-body behavior of polaritons formed from electron-hole pairs strongly coupled to photons in a two-dimensional semiconductor microcavity. We use a microscopic mean-field BCS theory that describes polariton condensation in quasi-equilibrium across the full range of excitation densities. In the limit of vanishing density, we show that our theory recovers the exact single-particle properties of polaritons, while at low densities it captures non-linear polariton-polariton interactions within the Born approximation. For the case of highly screened contact interactions between charge carriers, we obtain analytic expressions for the equation of state of the many-body system. This allows us to show that there is a photon resonance at a chemical potential higher than the photon cavity energy, where the electron-hole pair correlations in the polariton condensate become universal and independent of the details of the carrier interactions. Comparing the effect of different ranged interactions between charge carriers, we find that the Rytova-Keldysh potential (relevant to transition metal dichalcogenides) offers the best prospect of reaching the BCS regime, where pairs strongly overlap and the minimum pairing gap occurs at finite momentum. Finally, going beyond thermal equilibrium, we argue that there are generically two polariton branches in the driven-dissipative system and we discuss the possibility of a density-driven exceptional point within our model.

1 citation
Scattering and Strebel graphs

Pronobesh Maity

SciPost Phys. 13, 010 (2022) · published 26 July 2022 | · pdf

We consider a special scattering experiment with n particles in $\mathbb{R}^{n-3,1}$. The scattering equations in this set-up become the saddle-point equations of a Penner-like matrix model, where in the large $n$ limit, the spectral curve is directly related to the unique Strebel differential on a Riemann sphere with three punctures. The solutions to the scattering equations localize along different kinds of graphs, tuned by a kinematic variable. We conclude with a few comments on a connection between these graphs and scattering in the Gross-Mende limit.

1 citation

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