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arXiv:2110.08540 · Journal of Physics Conference Series

Quantum Correlations in Jahn-Teller Molecular Systems Simulated with Superconducting Circuits

AH Pedram, Onur Pusuluk, Özgür Esat Müstecaplıoğlu

Published Feb 1, 2022• 0 citations
arXivHTMLPDF

Abstract

Abstract We explore quantum correlations, in particular, quantum entanglement, among vibrational phonon modes as well as between electronic and vibrational degrees of freedom in molecular systems, described by Jahn-Teller mechanism. Specifically, to isolate and simplify the phonon- electron interactions in a complex molecular system, the basis of our discussions is taken to be the proposal of simulating two-frequency Jahn- Teller systems using superconducting circuit quantum electrodynamics systems (circuit QED) by Tekin Dereli and co-workers in 2012. We evaluate the quantum correlations, in particular entanglement between the vibrational phonon modes, and present analytical explanations using a single privileged Jahn-Teller mode picture. Furthermore, spin-orbit entanglement or quantum correlations between electronic and vibrational degrees of freedom are examined. We conclude by discussing experimental feasibility to detect such quantum correlations, considering the dephasing and decoherence in state-of-the-art superconducting two-level systems (qubits).

DOI
10.1088/1742-6596/2191/1/012018

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Abstract We explore quantum correlations, in particular, quantum entanglement, among vibrational phonon modes as well as between electronic and vibrational degrees of freedom in molecular systems, described by Jahn-Teller mechanism. Specifically, to isolate and simplify the phonon- electron interactions in a complex molecular system, the basis of our discussions is taken to be the proposal of simulating two-frequency Jahn- Teller systems using superconducting circuit quantum electrodynamics systems (circuit QED) by Tekin Dereli and co-workers in 2012. We evaluate the quantum correlations, in particular entanglement between the vibrational phonon modes, and present analytical explanations using a single privileged Jahn-Teller mode picture. Furthermore, spin-orbit entanglement or quantum correlations between electronic and vibrational degrees of freedom are examined. We conclude by discussing experimental feasibility to detect such quantum correlations, considering the dephasing and decoherence in state-of-the-art superconducting two-level systems (qubits).
Atoms confined in optical tweezer arrays constitute a platform for the implementation of quantum computers and simulators. State-dependent operations are realized by exploiting electrostatic dipolar interactions that emerge, when two atoms are simultaneously excited to high-lying electronic states, so-called Rydberg states. These interactions also lead to state-dependent mechanical forces, which couple the electronic dynamics of the atoms to their vibrational motion. We explore these vibronic couplings within an artificial molecular system in which Rydberg states are excited under so-called facilitation conditions. This system, which is not necessarily self-bound, undergoes a structural transition between an equilateral triangle and an equal-weighted superposition of distorted triangular states (Jahn-Teller regime) exhibiting spin-phonon entanglement on a micrometer distance. This highlights the potential of Rydberg tweezer arrays for the study of molecular phenomena at exaggerated length scales.
We investigate the simulation of Jahn-Teller models with two nondegenerate vibrational modes using a circuit QED architecture. Typical Jahn-Teller systems are anisotropic and require at least a two-frequency description. The proposed simulator consists of two superconducting lumped-element resonators interacting with a common flux qubit in the ultrastrong coupling regime. We translate the circuit QED model of the system to a two-frequency Jahn-Teller Hamiltonian and calculate its energy eigenvalues and the emission spectrum of the cavities. It is shown that the system can be systematically tuned to an effective single-mode Hamiltonian from the two-mode model by varying the coupling strength between the resonators. The flexibility in manipulating the parameters of the circuit QED simulator permits the isolation of the effective single-frequency and pure two-frequency effects in the spectral response of Jahn-Teller systems.
We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The $E\ensuremath{\bigotimes}\ensuremath{\beta}$ system models the coupling of a two-level electronic system, or qubit, to a single-oscillator mode, while the $E\ensuremath{\bigotimes}\ensuremath{\epsilon}$ models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the $E\ensuremath{\bigotimes}\ensuremath{\beta}$ system, the ground states of the $E\ensuremath{\bigotimes}\ensuremath{\epsilon}$ model always exhibit entanglement. For the $E\ensuremath{\bigotimes}\ensuremath{\beta}$ case we aim to clarify results from previous work, alluding to a link between the ground-state entanglement characteristics and a bifurcation of a fixed point in the classical analog. In the $E\ensuremath{\bigotimes}\ensuremath{\epsilon}$ case we make use of an ansatz for the ground state. We compare this ansatz to exact numerical calculations and use it to investigate how the entanglement is shared between the three system degrees of freedom.
Jahn-Teller systems exhibit strong coupling between the electronic and nuclear degrees of freedom. We analyse how linear and quadratic coupling affect the electron-nuclear entanglement in the E⊗ϵE\otimes \epsilonE⊗ϵ system. A measure of quantum entanglement, recently developed by Shimony [Ann. New York Acad. Sci. 755, 675 (1995)], is used. States in the adiabatic regime with quadratic coupling are analysed. The electron-nuclear entanglement in vibronic states of the linear Exe model is calculated numerically. The physical significance of electron-nuclear entanglement is discussed in terms of reduction factors and magnetic vibrational circular dichroism.
This review emphasizes the physical principles underlying the dephasing of nonstationary vibrational states of molecules with multiple vibrational degrees of freedom. The motion of atoms within molecules can be described to a very good approximation by a many-level system of coupled anharmonic quantized oscillators. The separation of electronic and nuclear timescales, combined with weak symmetry breaking inherent in molecular structures, guarantees that the Hamiltonian can always be cast in a form that is local in the quantum state space of the molecular vibrations. The resulting nonexponential dephasing dynamics can be controlled with external fields to stabilize nonstationary quantum states, and both quantum–classical and fully quantum control formalisms are described. Coupled molecular vibrations interacting with external fields also offer prospects for quantum computing because vibrational level spacings can be made very large compared to thermal noise, and relaxation mechanisms such as infrared fluorescence are many orders of magnitude slower than the timescales required for coherence transfer. Finally, a toy model that provides insights into the interaction of vibrational degrees of freedom with 'solvent' modes is also discussed, and exhibits nonexponential dynamics in certain regimes.
Superconducting quantum devices have drawn the attention of physicists greatly in recent years, not only because they are one of the most favorable candidates for developing a solid state quantum computer, but also because they can be employed as test systems for understanding quantum mechanics at nearly macro scale. Superconducting quantum devices can be divided into two groups: the superconducting resonators (linear devices), which have equally spaced discrete energy levels, and the artificial atoms (non-linear devices) consisting of Josephson junctions which have unequally spaced discrete energy levels. By combining these two kinds of devices together, a solid state counterpart of optical cavity quantum electrodynamics (QED) known as circuit QED emerges. Experiments of cavity QED and quantum optics can be reproduced in either circuit QED systems or in bare superconducting artificial atoms. As an example, we have observed the Autler-Townes effect in a three-level artificial atom called phase qutrit. \nMore than one decade has passed since the first experimental demonstration of superconducting two-level artificial atom (qubit). However, to build a practical quantum computer with thousands of superconducting qubits there is still a long way to go (we are at the stage of three qubits now). One of the main obstacles preventing us from scaling up a superconducting quantum computer, as well as some other kinds of quantum computers, has been decoherence, which is believed to be dominated by the low frequency noise due to the two-level system (TLS) fluctuators located inside the Josephson junction barrier. We have experimentally simulated the dynamics of a qubit longitudinally coupled to a randomly fluctuating TLS. A phenomenon known as motional averaging has been observed. \nIn this thesis, theoretical models for decoherence in both resonator and artificial atoms have been established and used for explaining phenomena observed in the experiments performed in our laboratory. The phenomenon of decoherence in coupled bipartite systems has been also studied, and besides the already known entanglement sudden death phenomenon, stable entanglement (robust under decoherence) generated from an arbitrary initial state has been found in these systems.