Session N14: Quantum Quenches and Heat Transport

Exceptions to Fourier's Law at the Macroscale

 For the past two centuries, heat conduction within materials has been widely described as diffusion according to Fourier's law, with exceptions only observed at the nanoscale. However, this study aims to challenge the prevailing understanding of heat conduction by investigating its limitations at the macroscale. To achieve this, a home-built VacuThermoStretch IR System is utilized to conduct steady and pulse heating experiments. The results reveal anomalous temperature distributions and thermal energy propagation that cannot be explained by the classical Fourier's Law. These anomalies are observed across a range of materials, including slow amorphous polymer glass, crosslinked polymer rubber, and semicrystalline polymers, as well as fast metals. This suggests new strategies of heat transfer design.   

Non Equilibrium Green's Function Approach for Modeling Carbon Nanotube Devices

We introduce a comprehensive theoretical framework to explore a non-equilibrium nanoelectromechanical system (NEMS) based on a fully suspended carbon nanotube (CNT) device. This complex system presents several significant modeling challenges, most notably: (1) the lifetime broadening of the electronic energy level; (2) Coulomb interactions; (3) the mechanical motion of the CNT and its influence on electronic states; and (4)  operation away from equilibrium.

Our approach innovatively addresses these challenges through the use of non-equilibrium Green's function (NEGF) formalism coupled with perturbation theory. Specifically, the lifetime broadening is encapsulated within the retarded Green's function by integrating energy-dependent self-energies, that account for strong coupling with source and drain Fermi reservoirs. Coulomb interactions are systematically included via additional self-energy terms thereby capturing electron-electron interactions. The mechanical motion of the CNT is modeled, introducing an explicit displacement-dependent term that enables us to derive equations for effective resonance frequencies.

The framework is mathematically rigorous and allows for the derivation of the spectral function for the density of available electronic states and current flowing through the device. 

By meticulously incorporating lifetime broadening, Coulomb interactions, mechanical displacements, and out of equilibrium effects, our theoretical construct provides a robust and comprehensive approach to analyze the transport phenomena in NEMS, laying the groundwork for future experimental validations and technological applications.   

Scaling of energy and power in a large quantum battery-charger model

We investigate a theoretical quantum battery-charger model, focusing on its potential emulation on concrete experimental platforms. Using a large-spin representation, we first obtain the analytical form of the energy E_B(t) and power P_B(t), and their maximum values E^max_B and P^max_B, of the battery part by means of the antiferromagnetic Holstein-Primakoff transformation within the low-energy approximation. In this case, our results show that superextensive scaling behavior of  P^max_B ensues. By further combining these with the ones obtained via exact diagonalization, we classify the dynamics of various physical quantities, including the entanglement between the battery and charger parts for system sizes encompassing over 10 000 qubits. Finally, by checking a diverse set of system configurations, including either a fixed battery size with a growing number of charger qubits or when both parts simultaneously grow, we classify the system size scalings of E^max_B and P^max_B, relating it with the entanglement entropy in the system. In agreement with the analytical results, robust superextensive behavior of P^max_B is also observed in this case. Our work provides an overall guide for expected features in experiments of quantum batteries emulated in multi-qubit platforms, in particular ones that exhibit long-range couplings.   

Harnessing synthetic axions to probe a cosmological axion

Synthetic axions in topological insulators and Weyl semimetals couple to electromagnetism via a topological Chern-Simons term, and so do cosmological axions which are compelling dark matter candidates. Therefore, synthetic and cosmological axions couple indirectly via intermediate states of two photons. We introduce a non-equilibrium effective field theory description of their hybridization or mixing in a medium. We find that a cosmological axion condensate may induce a synthetic axion condensate, and either condensate will induce a topological Chern-Simons condensate in the intermediate photon states. Furthermore, the axion(s) two-point correlation function features an emergent coherence, and displays quantum beats akin to a three level "V" system from a "which-path" interference between the (quasi) normal modes. We analyzed the correlation functions of the intermediate two-photon state and highlighted distinct features that indicate the existence of Chern-Simons condensate. These results may suggest the possibility of harnessing emergent axion quasiparticles in condensed matter systems to probe the cosmological axion as well as new tools to characterize properties of materials with axionic excitations.   

Memory effects in the energy dissipation of anharmonic solids

Dissipation is commonly described by a system-bath coupling. However, in systems with a macroscopic number of degrees of freedom, the bath can be the system itself, i.e., for excitations that only involve a subset of degrees of freedom, the dissipation and decoherence is produced by interactions with the remaining degrees of freedom. We use a simple model of coupled harmonic oscillators to explore the effects of local dissipation that can arise from large isolated systems, without the need to invoke a bath. When the oscillator potentials are purely harmonic, the energy of the system is transmitted by ballistic phonons that can propagate through the crystal lattice without scattering. Impurities and anharmonicities introduce memory effects in the time evolution of the phonons with the consequent loss of coherence. The energy transmission goes from ballistic to diffusive. We use a Mori-Zwanzig projection to encode anharmonic terms to all orders into the memory function. The result is an analytical expression for energy dissipation from a localized initial perturbation that describes the transition from ballistic to diffusive. A thermal conductivity coefficient can be extracted from the analysis.    

Theoretical Investigation of non-Markovian Dynamics of an Optomechanical System Acting as an Autonomous Quantum Heat Engine

While new quantum technologies are being developed at an accelerating pace, the field of quantum thermodynamics [1] is attracting a lot of attention, as researchers are discovering a plethora of phenomena in quantum systems subjected to thermal fluctuations. The key example of such a quantum device is the quantum heat engine (QHE) [2] --- a device operating at the quantum level, designed to interact with heat reservoirs and extract work from heat flow. We propose utilizing a well-known quantum device, the optomechanical system, in a novel manner to realize an autonomous QHE.

In this work, we show that when the optical cavity of an optomechanical system is coupled to non-Markovian heat baths, it is possible to reach excitation generation in the mechanical mode. We study the classical analogue of the equations of motion of the optomechanical system with the key difference that instead of coherent drive, we subject the optical cavity only to thermal fluctuations from two baths with different temperatures. Further, we shall not resort to Markovian approximation, but rather study the full non-Markovian dynamics with coloured quantum noise. We derive quasiclassical Langevin equations describing the intricate non-linear dynamics of the system and study their solutions. 

[1] S. Deffner and S. Campbell. Morgan and Claypool, 2019.

[2] H. Goswami and U. Harbola. Phys. Rev. A, 88:013842, Jul 2013

[3] A. Schmid, Jour. of Low Temp. Phys, vol. 49, no. 5-6, Dec. 1982    

Non-equilibrium Quantum Field Theory for Thermal Inhomogeneity in Thermoelectric Devices

We generalized the standard non-equilibrium field theory framework to incorporate a temperature gradient across a thermoelectric device. The framework uses a temperature-dependent pseudo-Hamiltonian generated from the exact density matrix in the presence of non-uniform temperatures. We proposed a perturbation theory for otherwise free particles with small temperature gradients in long wires and obtained the Fermi and Boson distribution functions to first order accuracy. In addition, non-linear thermal conductivity as a function of temperature difference is calculated. The framework should be adaptable to more general cases of temperature inhomogeneities in either fermionic or bosonic systems.   

Inhomogeneous charge density wave states induced by quantum quenches

We study the post-quench dynamics of the charge-density-wave (CDW) orders in the t-V model. The ground state of the system is characterized by a checkerboard modulation of fermion numbers due to a perfect nesting of the Fermi surface at half-filling. An efficient real-space von Neumann equation method is employed to investigate the quench dynamics of an initially perfect CDW state. Our large-scale simulations reproduce the three distinct post-quench behaviors, the phase-locked coherent oscillation, Landau-damped, and over-damped oscillations. Moreover, we observe the emergence of intriguing inhomogeneous CDW states for quenches with particularly large increase of interaction strength. We perform quantitative characterizations of the quench-induced inhomogeneity, and its relationship with the depth of quenched interactions. Our results demonstrate the spatial inhomogeneity in the quench dynamics of Ising-type order, which is perhaps one of the simplest examples of symmetry breaking, and underscore the importance of dynamical inhomogeneity in quantum quenches of many-body systems with more complex orders.   

Quantum Interference Enhancement of the Spin-dependent Thermoelectric Response

We investigate the influence of quantum interference and broken spin-symmetry on the thermoelectric response of node-possessing junctions, finding a dramatic enhancement of the spin-thermopower (S_s), figure-of-merit (Z_sT), and maximum thermodynamic efficiency (η_s^max) caused by destructive quantum interference. Using many-body and single-particle methods, we calculate the response of 1,3-benzenedithiol and cross-conjugated molecule-based junctions subject to an applied magnetic field, finding nearly universal behavior over a broad range of junction parameters withS_s, Z_sT, and η_s^max reaching peak values of 2π/√3 (k/e), 1.51, and 28% of Carnot efficiency, respectively. The influence of off-resonant thermal channels (e.g. phonon heat transport) on the quantum interference-enhanced spin-response is also investigated.   

Ultrafast transient absorption spectroscopy of strongly correlated Mott insulators

We applied time-resolved transient absorption spectroscopy to systematically investigate the ultrafast optical responses of condensed matter systems. Under an intense pump pulse, absorption spectra indicate that the noninteracting electrons of band insulators produce a field-induced redshift, known as the dynamical Franz-Keldysh effect, as commonly expected. In contrast to band insulators, in Mott insulators, unconventional spectra are observed which do not fully reflect the dynamical Franz-Keldysh effect. While the spectra still exhibit fishbonelike structures mimicking the dynamical Franz-Keldysh effect, they show a negative difference absorption below the band edge, rendering a blueshift. In addition, the decomposed calculation reveals that the negative difference absorption is mainly contributed from the creation and the annihilation of transient double occupancy, implying that the unconventional spectra are purely driven by the electron correlations. These demonstrated unconventional responses can guide us to better understanding of the correlation-originated ultrafast electron dynamics in condensed matter systems.   

Quantum refrigeration powered by dephasing in a superconducting circuit

While dephasing noise frequently presents obstacles for quantum devices, it can become an asset in the context of quantum refrigerators. Quantum thermal machines have in recent years garnered more attention, but their implementation is hindered by the difficulties in measuring tiny heat flows. Here we demonstrate a novel quantum thermal machine that leverages dephasing noise to fuel a cooling engine in steady state. The device exploits symmetry selective couplings between a superconducting artificial molecule, comprised of two strongly flux tunable transmon qubits, and two microwave waveguides. These waveguides act as thermal reservoirs of different temperatures, which are regulated by employing synthesized thermal fields. The dephasing is controlled by injecting white noise through a third channel that is longitudinally coupled to the molecule. The interplay between individual thermalization to the baths and dephasing noise produces a heat current between the two baths, which we measure with a resolution below 1 aW using interleaved power spectral density measurements. By varying the temperature ratio of the thermal reservoirs, we demonstrated that the device can be operated as a quantum heat engine, thermal accelerator, and refrigerator. Our findings show the successful operation of a Brownian refrigerator and the simultaneous measurement of heat flows to multiple baths, opening new avenues for investigating quantum thermal machines in circuit quantum electrodynamics.   

Non-equilibrium variable range hopping under DC bias in disordered electronic systems.

Variable range hopping is a mechanism of transport of electrons in a disordered electronic system which typically behave as insulators due to Anderson localization. In this study, we develop a theory of field assisted variable range hopping as a mechanism for insulator-metal transition in disordered systems. We develop a quantum mechanical model consisting of a 1D disordered insulating tight binding chain coupled to a dissipative fermionic bath and apply electric field across the chain. Our model shows the Mott 1/2-law in equilibrium. Under electric field we compute the IV characteristics using non-equilibrium green's function method which shows us a non-linear increase in the conductance with electric field. Our study indicates a disorder range in which the system shows variable range hopping and then goes into a transition from an typically insulator behavior to a metallic behavior.   

Boundary Kondo Impurity with PT-symmetry and Beyond: a Bethe Ansatz approach

The development of cold atom experimental techniques and superconducting quantum computers allows the experimental study of dissipative 1D quantum many-body systems. These dissipative systems are often modeled by non-Hermitian Hamiltonians that typically arise when one wishes to provide an effective description of an open system coupled to an external environment.

This raises interesting questions about how these open systems differ from closed ones and what new physics would emerge in such systems.  In this work, we study a one-dimensional conducting wire attached with complex coupling constants to Kondo impurities one at each edge, the two coupling constants being complex conjugates of each other leading to a  PT-symmetric  Hamiltonian. We also investigate how the physics changes when the PT symmetry is broken.

We solve the non-Hermitian Hamiltonian exactly with the Bethe Ansatz approach, obtain the spectrum of its eigenstates, and analyze their stability.  We show that new phases arise, phases that do not exist in the conventional Kondo problem, and study boundary phase transitions between them.