The Polaron: Ground State, Excited States, and Far from Equilibrium

Yi-Fan Qu, Pavel E. Dolgirev, Eugene Demler +1 more

We develop a non-Gaussian variational approach that enables us to study both equilibrium and far-from-equilibrium physics of the two-dimensional Fermi polaron. This method provides an unbiased analysis of the polaron-to-molecule phase transition without relying on truncations in the total number of particle-hole excitations. Our results—which include the ground-state energy and quasiparticle residue—are in qualitative agreement with the known Monte Carlo calculations. The main advantage of the non-Gaussian states compared to conventional numerical methods is that they enable us to explore long-time polaron evolution and, in particular, study various spectral properties accessible to both solid-state and ultracold atom experiments. We design two types of radiofrequency spectroscopies to measure polaronic and molecular spectral functions. Depending on the parameter regime, we find that these spectral functions and fermionic density profiles near the impurity either display long-lived oscillations between the repulsive and attractive polaron branches or exhibit fast relaxational dynamics to the molecular state.

Hua Chen

L. F. Lemmens, J. T. Devreese

Shi, T., Eugene Demler, J. I. Cirac

We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian states by including generalized canonical transformations between the fields. The key advantage of such states compared to simple Gaussian states is presence of non-factorizable correlations and the possibility of describing states with strong entanglement between particles. In contrast to the commonly used canonical transformations, such as the polaron or Lang-Firsov transformations, we allow parameters of the transformations to be time dependent, which extends their regions of applicability. We derive equations of motion for the parameters characterizing the states both in real and imaginary time using the differential structure of the variational manifold. The ground state can be found by following the imaginary time evolution until it converges to a steady state. Collective excitations in the system can be obtained by linearizing the real-time equations of motion in the vicinity of the imaginary time steady-state solution. Our formalism allows us not only to determine the energy spectrum of quasiparticles and their lifetime, but to obtain the complete spectral functions and to explore far out of equilibrium dynamics such as coherent evolution following a quantum quench. We illustrate and benchmark this framework with several examples: a single polaron in the Holstein and Su-Schrieer-Heeger models, non-equilibrium dynamics in the spin-boson and Kondo models, the superconducting to charge density wave phase transitions in the Holstein model.

Xu-Fang Bai, Lei Chen

Recently, the measurement scheme of quantum dot qubit decocoherence quantized by the longitudinal optical (LO) phonon spontaneous emission rate has attracted the attention and discussion of many researchers. However, it is not difficult to see that the above-mentioned measurement scheme still has some insufficient and imperfect aspects that are to be studied urgently. Considering from the physical mechanism, the essence of the above scheme is to quantify the decoherence time of qubit by using the excited state decay time or excited state lifetime of the polaron. However, so far, there is little research on how the ground state decay time and ground state lifetime of two-state polaron affect the coherence of qubit. There is no doubt that this is an equally important research topic. This is because, firstly, for the coherence of the quantum state of polaron, both the decay of the excited state and the decay of the ground state will destroy or attenuate the qubit coherence, secondly, the transition rate of the two-state polaron from the ground state to the excited state after absorbing an LO phonon is also a function quantifying the qubit decoherence time of two-state system of which the inverse is called the ground state decay time or the ground state lifetime. It may be called a measure of qubit decoherence time quantized by the ground state decay time or ground state lifetime of polaron. In this article, the ground-state and excited-state energy and wave function of the magnetopolaron in a donor-center quantum dot with asymmetric Gaussian potential are derived by Lee-Low-Pines transformation and Pekar-type variational methodd, and then the two-level structure for a qubit is constructed. The measure of qubit decoherence time of quantum dots quantified by ground state decay time of two-state polaron is established, which is compared with the well-known measure of qubit decoherence time of quantum dots quantified by polaron excited state decay time, and their physical mechanisms are revealed. By studying the influence of dielectric constant ratio, electro-phonons coupling constant, temperature and electromagnetic field on the ground state lifetime of magnetopolaron in the donor-center quantum dots with asymmetric Gaussian potential, the influences of material properties, temperature, electromagnetic field and other environmental factors on qubit decoherence of quantum dots are revealed, thereby revealing the mechanism of qubit decoherence caused by LO phonon effect.

J. T. Devreese, R. Evrard