arXiv subjects

J. K. Freericks

Publications and source records attributed to J. K. Freericks.

At least 55 records · Page 3Linked to original sources

arXiv2018

Interpreting pulse-shape effects in pump-probe spectroscopies

The effect of the pulse-shape on pump-probe spectroscopies is examined for the simplest model of noninteracting fermions on an infinite-dimensional hypercubic lattice. The probe-modified density of states follows the time evolution of the pump and displays narrowing and Floquet-like sidebands at the pump maximum, whereas the photoelectron spectra are also strongly affected by the nonequilibrium occupation of the single-particle states due to the excitation from the pump. The nonequilibrium Raman cross section is derived, and the nonresonant one in both the $A_{1\mathrm{g}}$ and $B_{1\mathrm{g}}$ symmetries contains a number of peaks at the pump maximum, which can be attributed to an interference effect or Brillouin scattering off the time variations of the stress tensor. Both the "measured" occupation of single-particle states and the ratio of Stokes to anti-Stokes peaks are strongly modified by the probe-pulse width, which must be included in the interpretation of experimental results.

cond-mat.str-el↗

arXiv2018

X-Ray Photoemission Spectroscopy in the Falicov-Kimball model

We calculate the finite temperature X-ray photoemission spectroscopy for the Falicov-Kimball model using a Weiner-Hopf sum equation approach. In the metallic state, the core-hole spectral function shows two side peaks corresponding to the creation of a core-hole on an empty site (or a doubly occupied site) and also has two nearly degenerate central peaks (because of our choice of the model parameters) corresponding to the creation of a core-hole on a singly occupied site. The nearly doubly degenerate central peaks merge into a single peak at higher temperatures. In the insulating state, we obtain two peaks and a strongly temperature dependent low-energy peak corresponding to the creation of a core-hole on a thermally excited empty site. These results for the insulating state should be similar to those of the more general Hubbard model. Also, the strong correlations suggest that even without any additional broadening due to Auger like processes, the core-hole lifetime will be short.

cond-mat.str-el↗

arXiv2018

Stroboscopic Tests for Thermalization of Electrons in Pump/Probe Experiments

One of the goals of pump/probe spectroscopies is to determine how electrons relax after they have been driven out of equilibrium. It is challenging to determine how close electrons are to a thermal state solely by fitting their distribution to a Fermi-Dirac distribution. Instead, we propose that one compare the effective temperatures of both fermions and collective bosonic modes (derived from the fermions) to determine the distance from a thermal state. Measurements of effective fermionic and bosonic temperatures can be achieved directly via photoemission and nonresonant Raman scattering. Their difference quantifies the distance from thermal equilibrium.

cond-mat.str-el↗

arXiv2018

Emergence of Floquet Behavior for Lattice Fermions Driven by Light Pulses

As many-body Floquet theory becomes more popular, it is important to find ways to connect theory with experiment. Theoretical calculations can have a periodic driving field that is always on, but experiment cannot. Hence, we need to know how long a driving field is needed before the system starts to look like the periodically driven Floquet system. We answer this question here for noninteracting band electrons in the infinite-dimensional limit by studying the properties of the system under pulsed driving fields and illustrating how they approach the Floquet limit. Our focus is on determining the minimal pulse lengths needed to recover the qualitative and semiquantitative Floquet theory results.

cond-mat.str-el↗

arXiv2018

Verification of a many-ion simulator of the Dicke model through slow quenches across a phase transition

We use a self-assembled two-dimensional Coulomb crystal of $\sim 70$ ions in the presence of an external transverse field to engineer a simulator of the Dicke Hamiltonian, an iconic model in quantum optics which features a quantum phase transition between a superradiant/ferromagnetic and a normal/paramagnetic phase. We experimentally implement slow quenches across the quantum critical point and benchmark the dynamics and the performance of the simulator through extensive theory-experiment comparisons which show excellent agreement. The implementation of the Dicke model in fully controllable trapped ion arrays can open a path for the generation of highly entangled states useful for enhanced metrology and the observation of scrambling and quantum chaos in a many-body system.

quant-ph↗

arXiv2018

Nonequilibrium Electron Dynamics In Pump-Probe Spectroscopy: Role Of Excited Phonon Populations

We study the role of excited phonon populations in the relaxation rates of nonequilibrium electrons using a nonequilibrium Green's function formalism. The transient modifications in the phononic properties are accounted for by self-consistently solving the Dyson equation for the electron and phonon Green's functions. The pump induced changes manifest in both the electronic and phononic spectral functions. We find that the excited phonon populations suppress the decay rates of nonequilibrium electrons due to enhanced phonon absorption. The increased phonon occupation also sets the nonequilibrium decay rates and the equilibrium scattering rates apart. The decay rates are found to be time-dependent, and this is illustrated in the experimentally observed population decay of photoexcited $\mathrm{Bi}_{1.5}\mathrm{Sb}_{0.5} \mathrm{Te}_{1.7}\mathrm{Se}_{1.3}$.

cond-mat.str-el↗

arXiv2018

General principles for the non-equilibrium relaxation of populations in quantum materials

We examine the problem of how excited populations of electrons relax after they have been excited by a pump. We include three of the most important relaxation processes: (i) impurity scattering; (ii) Coulomb scattering; and (iii) electron-phonon scattering. The relaxation of an excited population of electrons is one of the most fundamental processes measured in pump/probe experiments, but its interpretation remains under debate. We show how several common assumptions about non-equilibrium relaxation that are pervasive in the field may not hold under quite general conditions. The analysis shows that non-equilibrium relaxation is more complex than previously thought, but it yields to recently developed theoretical methods in non-equilibrium theory. In this work, we show how one can use many-body theory to properly interpret and analyze these complex systems. We focus much of the discussion on implications of these results for experiment.

cond-mat.stat-mech↗

arXiv2017

Exploring adiabatic quantum dynamics of the Dicke model in a trapped ion quantum simulator

We use a self-assembled two-dimensional Coulomb crystal of $\sim 70$ ions in the presence of an external transverse field to engineer a quantum simulator of the Dicke Hamiltonian. This Hamiltonian has spin and bosonic degrees of freedom which are encoded by two hyperfine states in each ion and the center of mass motional mode of the crystal, respectively. The Dicke model features a quantum critical point separating two distinct phases: the superradiant (ferromagnetic) and normal (paramagnetic) phases. We experimentally explore protocols that aim to adiabatically prepare the superradiant ground state, a spin-boson cat state with macroscopic phonon occupation, which is well-suited for enhanced metrology and quantum information processing. We start in the normal phase, with all spins aligned along a large transverse field and ramp down the field across the critical point following various protocols. We measure the spin observables, both experimentally and in our simulations to characterize the state of the system at the end of the ramp. We find that under current operating conditions an optimally designed ramp is not sufficient to achieve significant fidelity with the superradiant ground state. However, our theoretical investigation shows that slight modifications of experimental parameters, together with modest reductions in decoherence rates and thermal noise can increase the cat-state fidelity to $\sim 75\%$ for $N \sim 20$ spins. Our results open a path for the use of large ensembles of trapped ions as powerful quantum sensors and quantum computers.

quant-ph↗

arXiv2017

Teaching quantum mechanics to over 14,000 nonscientists

We describe a new style of MOOC designed to engage students with an immersive multimedia environment including text, images, video lectures, computer-based simulations, animations, and tutorials. Quantum Mechanics for Everyone is currently running on EdX and has been successful by a number of different measures. It illustrates both how one can teach complex quantum phenomena to nonscientists and how one can develop high quality interactive computer simulations that engage the students and can be widely deployed.

physics.ed-ph↗

arXiv2017

Incorporating the Stern-Gerlach delayed-choice quantum eraser into the undergraduate quantum mechanics curriculum

As "Stern-Gerlach first" becomes the new paradigm within the undergraduate quantum mechanics curriculum, we show how one can extend the treatment found in conventional textbooks to cover some of the exciting new developments within the quantum field. Namely, we illustrate how one can employ Dirac notation and conventional quantum rules to describe a delayed choice variant of the quantum eraser which is realized within the Stern-Gerlach framework. Covering this material, allows the instructor to reinforce notions of changes of basis functions, quantum superpositions, quantum measurement, and the complementarity principle as expressed in whether we know "which-way" information or not. It also allows the instructor to dispel common misconceptions of when a measurement occurs and when a system is in a superposition of states. We comment at the end how a similar methodology can be employed when the more conventional two-slit experiment is treated.

physics.ed-ph↗

arXiv2017

Spin and pseudospin towers of the Hubbard model on a bipartite lattice

In 1989, Lieb proved two theorems about the Hubbard model. One showed that the ground state of the attractive model was a spin singlet state ($S=0$), was unique, and was positive definite. The other showed that the ground state of the repulsive model on a bipartite lattice at half-filling has a total spin given by $|(N_A-N_B)/2|$, corresponding to the difference of the number of lattice sites on the two sublattices divided by two. In the mid to late 1990's, Shen extended these proofs to show that the pseudospin of the attractive model was minimal until the electron number equaled $2N_A$ where it became fixed at $J=|(N_A-N_B)/2|$ until the filling became $2N_B$, where it became minimal again. In addition, Shen showed that a spin tower exists for the spin eigenstates for the half-filled case on a bipartite lattice. The spin tower says the minimal energy state with spin $S$ is higher in energy than the minimal energy state with spin $S-1$ until we reach the ground-state spin given above. One long standing conjecture about this model remains, namely does the attractive model have such a spin tower for all fillings, which would then imply that the repulsive model has minimal pseudopsin in its ground state. While we do not prove this last conjecture, we provide a quick review of this previous work, provide a constructive proof of the pseudospin of the attractive model ground state, and describe the challenges with proving the remaining open conjecture.

cond-mat.str-el↗

arXiv2017

Amplitude mode oscillations in pump-probe photoemission spectra from a d-wave superconductor

Recent developments in the techniques of ultrafast pump-probe photoemission have made possible the search for collective modes in strongly correlated systems out of equilibrium. Including inelastic scattering processes and a retarded interaction, we simulate time- and angle- resolved photoemission spectroscopy (trARPES) to study the amplitude mode of a d-wave superconductor, a collective mode excited through the nonlinear light-matter coupling to the pump pulse. We find that the amplitude mode oscillations of the d-wave order parameter occur in phase at a single frequency that is twice the quasi-steady-state maximum gap size after pumping. We comment on the necessary conditions for detecting the amplitude mode in trARPES experiments.

cond-mat.supr-con↗

arXiv2017

Relationship between the transverse-field Ising model and the XY model via the rotating-wave approximation

In a large transverse field, there is an energy cost associated with flipping spins along the axis of the field. This penalty can be employed to relate the transverse-field Ising model in a large field to the XY model in no field (when measurements are performed at the right stroboscopic times). We describe the details for how this relationship works and, in particular, we also show under what circumstances it fails. We examine wavefunction overlap between the two models and observables, such as spin-spin Green's functions. In general, the mapping is quite robust at short times, but will ultimately fail if the run time becomes too long. There is also a trade-off between the length of time one can run a simulation out to and the time jitter of the stroboscopic measurements that must be balanced when planning to employ this mapping.

cond-mat.quant-gas↗

arXiv2017

Thermoelectric transport parallel to the planes in a multilayered Mott-Hubbard heterostructure

We present a theory for charge and heat transport parallel to the interfaces of a multilayer (ML) in which the interfacing gives rise the redistribution of the electronic charges. The ensuing electrical field couples self-consistently to the itinerant electrons, so that the properties of the ML crucially depend on an interplay between the on-site Coulomb forces and the long range electrostatic forces. The ML is described by the Falicov-Kimball model and the self-consistent solution is obtained by iterating simultaneously the DMFT and the Poisson equations. This yields the reconstructed charge profile, the electrical potential, the planar density of states, the transport function, and the transport coefficients of the device. We find that a heterostructure built of two Mott-Hubbard insulators exhibits, in a large temperature interval, a linear conductivity and a large temperature-independent thermopower. The charge and energy currents are confined to the central part of the ML. Our results indicate that correlated multilayers have the potential for applications; by tuning the band shift and the Coulomb correlation on the central planes, we can bring the chemical potential in the immediate proximity of the Mott-Hubbard gap edge and optimize the transport properties of the device. In such a heterostructure, a small gate voltage can easily induce a MI transition. This switching does not involve the diffusion of electrons over macroscopic distances and it is much faster than in ordinary semiconductors. Furthermore, the right combination of strongly correlated materials with small ZT can produce, theoretically at least, a heterostructure with a large ZT.

cond-mat.str-el↗

arXiv2017

Enhancing quantum order with fermions by increasing species degeneracy

One of the challenges for fermionic cold atom experiments in optical lattices is to cool the systems to low enough temperature that they can form quantum degenerate ordered phases. In particular, there has been significant work in trying to find the antiferromagnetic phase transition of the Hubbard model in three dimensions, without success. Here, we attack this problem from a different angle by enhancing the ordering temperature via an increase in the degeneracy of the atomic species trapped in the optical lattice. In addition to developing the general theory, we also discuss some potential systems where one might be able to achieve these results experimentally.

cond-mat.quant-gas↗

arXiv2017

Relaxation of nonequilibrium populations after a pump: the breaking of Mathiessen$'$s rule

From the early days of many-body physics, it was realized that the self-energy governs the relaxation or lifetime of the retarded Green$'$s function. So it seems reasonable to directly extend those results into the nonequilibrium domain. But experiments and calculations of the response of quantum materials to a pump show that the relationship between the relaxation and the self-energy only holds in special cases. Experimentally, the decay time for a population to relax back to equilibrium and the linewidth measured in a linear-response angle-resolved photoemission spectroscopy differ by large amounts. Theoretically, aside from the weak-coupling regime where the relationship holds, one also finds deviations and additionally one sees violations of Mathiessen$'$s rule. In this work, we examine whether looking at an effective transport relaxation time helps to analyze the decay times of excited populations as they relax back to equilibrium. We conclude that it may do a little better, but it has a fitting parameter for the overall scale which must be determined.

cond-mat.stat-mech↗

arXiv2016

Constant Matrix Element Approximation to Time-Resolved Angle-Resolved Photoemission Spectroscopy

We describe different approximations associated with employing a constant matrix element for the coupling of light to multiband electrons in the context of time-resolved angle-resolved photoemission spectroscopy (TR-ARPES). In particular, we demonstrate that the constant matrix approximation only holds for one of the coordinate representations, and changing to other bases, requires including nonconstant corrections to the matrix element. We also discuss some simplifying approximations, where a constant matrix element is employed in multiple bases, and the consequences of this further approximation (especially with respect to the TR-ARPES signal no longer being nonnegative). We also discuss issues related to gauge invariance of the final spectra.

cond-mat.str-el↗

arXiv2016

Exact time evolution of the asymmetric Hubbard dimer

We examine the time evolution of an asymmetric Hubbard dimer, which has a different on-site interaction on the two sites. The Hamiltonian has a time-dependent hopping term, which can be employed to describe an electric field (which creates a Hamiltonian with complex matrix elements), or it can describe a modulation of the lattice (which has real matrix elements). By examining the symmetries under spin and pseudospin, we show that the former case involves at most a 3 x 3 block---it can be mapped onto the time evolution of a time-independent Hamiltonian, so the dynamics can be evaluated analytically and exactly (by solving a nontrivial cubic equation). We also show that the latter case reduces to at most 2 x 2 blocks, and hence the time evolution for a single Trotter step can be determined exactly, but the time evolution generically requires a Trotter product.

cond-mat.str-el↗