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arXiv:2105.05749

Probing particle-particle correlation in harmonic traps with twisted light

Johanna I. Fuks, G. F. Quinteiro, Heiko Appel, P. I. Tamborenea

Published May 12, 2021• 1 citation
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Abstract

We explore the potential of twisted light as a tool to unveil many-body effects in parabolically confined systems. According to the Generalized Kohn Theorem, the dipole response of such a multi-particle system to a spatially homogeneous probe is indistinguishable from the response of a system of non-interacting particles. Twisted light however can excite internal degrees of freedom, resulting in the appearance of new peaks in the even multipole spectrum which are not present when the probe is a plane wave. We also demonstrate the ability of the proposed twisted light probe to capture the transition of interacting fermions into a strongly correlated regime in a one-dimensional harmonic trap. We report that by suitable choice of the probe's parameters, the transition into a strongly correlated phase manifests itself as an approach and ultimate superposition of peaks in the second order quadrupole response. These features, observed in exact calculations for two electrons, are reproduced in adiabatic Time Dependent Density Functional Theory simulations.

DOI
10.48550/arxiv.2105.05749

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We explore the potential of twisted light as a tool to unveil many-body effects in parabolically confined systems. According to the Generalized Kohn Theorem, the dipole response of such a multi-particle system to a spatially homogeneous probe is indistinguishable from the response of a system of non-interacting particles. Twisted light however can excite internal degrees of freedom, resulting in the appearance of new peaks in the even multipole spectrum which are not present when the probe is a plane wave. We also demonstrate the ability of the proposed twisted light probe to capture the transition of interacting fermions into a strongly correlated regime in a one-dimensional harmonic trap. We report that by suitable choice of the probe's parameters, the transition into a strongly correlated phase manifests itself as an approach and ultimate superposition of peaks in the second order quadrupole response. These features, observed in exact calculations for two electrons, are reproduced in adiabatic Time Dependent Density Functional Theory simulations.
We explore the potential of twisted light, a structured beam carrying orbital angular momentum, as a tool to unveil many-body effects in parabolically confined systems. According to the generalized Kohn theorem, the dipole response of such a multiparticle system to a spatially homogeneous probe is indistinguishable from the response of a system of noninteracting particles. Twisted light however can excite internal degrees of freedom, resulting in the appearance of new peaks in the multipole spectrum which are not present when the probe is a plane wave. We also demonstrate the ability of the proposed twisted light probe to capture the transition of interacting fermions into a strongly correlated regime in a one-dimensional harmonic trap. We report that, by suitable choice of the probe's parameters, the transition into a strongly correlated phase manifests itself as an approaching and ultimate superposition of peaks in the second-order quadrupole response. These features are observed in exact calculations for two electrons and well reproduced in adiabatic time-dependent density-functional theory simulations.
Abstract Many quantum phenomena responsible for key applications in material science and quantum chemistry arise in the strongly correlated regime. This is at the same time, a costly regime for computer simulations. In the limit of strong correlation analytic solutions exist, but as we move away from this limit numerical simulation are needed, and accurate quantum solutions do not scale well with the number of interacting particles. In this work we propose to use few-particle harmonic traps in combination with twisted light as a quantum emulator to investigate the transition into a strongly-correlated regime. Using both analytic derivations and numerical simulations we generalize previous findings on 2 Coulomb interacting fermions trapped in a one-dimensional harmonic trap to the case of 3 fermions. The 4 signatures of strong correlation we have identified in the one-dimensional harmonic trap are: (i) the ground state density is highly localized around N equilibrium positions, where N is the number of particles, (ii) the symmetric and antisymmetric ground state wavefunctions become degenerate, (iii) the von Neumann entropy grows, (iv) the energy spectrum is fully characterized by N normal modes or less. Our findings describe the low-energy behavior of electrons in quantum wires and ions in Paul traps. Similar features have also been reported for cold atoms in optical lattices.
The transition into a strongly-correlated regime of 3 fermions trapped in a one-dimensional harmonic potential is investigated. This interesting, but little-studied system, allows us to identify characteristic features of the regime, some of which are also present in strongly-correlated materials relevant to the industry. Furthermore, our findings describe the behavior of electrons in quantum dots, ions in Paul traps, and even fermionic atoms in one-dimensional optical lattices. Near the ground state, all these platforms can be described as fermions trapped in a harmonic potential. The correlation regime can be controlled by varying the natural frequency of the trapping potential, and to probe it, we propose to use twisted light. We identify 4 signatures of strong correlation in the one-dimensional 3-fermion trap, which are likely to be present for any number N of trapped fermions: i) the ground state density is strongly localized with N maximally separated peaks (Wigner Crystal) ii) the symmetric and antisymmetric ground state wavefunctions become degenerate (bosonization) iii) the von Neumann entropy grows, iv) the energy spectrum is fully characterized by N normal modes or less.
We present a theoretical study of nondipole excitation of a single trapped atom by twisted light. Special emphasis is placed on effects that arise from the interplay between internal (electronic) and vibrational (center-of-mass) degrees of freedom of an atom. In order to provide a fully quantum mechanical understanding of the excitation, we used the density-matrix approach based on the Liouville--von Neumann equation. The developed theory has been applied to the particular case of the $4s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\ensuremath{\rightarrow}3d\phantom{\rule{0.16em}{0ex}}^{2}D_{5/2}$ electric quadrupole (E2E2E2) transition in a 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion induced by Laguerre-Gaussian modes. It was found that the Rabi oscillations can show unconventional anharmonic behavior that is attributed to the strong coupling between vibrational levels of the trap. This effect is accompanied by the transfer of angular momentum to the center-of-mass motion and becomes most pronounced when the Rabi frequency is comparable to the trapping frequency.
Twisted light carries orbital angular momentum (OAM) and can drive excitations of confined, interacting electrons that are dark to uniform dipolar probes. Here we show how this ``beyond-Kohn's-Theorem'' optical channel can become a concrete control primitive for quantum computing. Correlation sectors in few-electron quantum dots -- characterized by the relative angular momentum quantum number -- form a tunable ladder of many-body states that are robust in the limited sense of symmetry-protected selection rules and persistent chiral spectroscopic fingerprints; full topological gap protection requires three or more electrons. A twisted-light pulse with prescribed OAM index and polarization provides fast optical write, read, and scalable addressing of these sectors via the selection rule Δ∣m∣=±(l+σ)Δ|m|=\pm(l+σ)Δ∣m∣=±(l+σ). In the analytically solvable Calogero (1/r21/r^21/r2) interaction limit, both the energy spectrum and the twisted-light matrix elements are closed-form functions of the interaction strength, allowing gate parameters (Rabi frequency, qubit frequency, anharmonicity, and leakage rates) to be written down explicitly. We map these results onto a universal single-qubit gate set, propose a concrete two-qubit entangling mechanism via state-dependent Coulomb coupling between adjacent dots, and identify the dominant decoherence channel (quadrupolar charge noise). A semi-analytic N=3N=3N=3 extension using the 1/N1/N1/N expansion provides a design-level scaffold for the topological roadmap, including quasihole sector addressing. The central operational message is that twisted light enables WRITE (pulse-create a correlation sector), READ (spectroscopically diagnose correlations), and SCALE (optical addressing via spatial light modulator) in a unified photonic control layer. Throughout, screened and Coulomb interactions preserve the same qualitative chiral fingerprints established in the solvable limit.
We study a strongly attractive system of a few spin-(1/2) fermions confined in a one-dimensional harmonic trap, interacting via two-body contact potential. Performing exact diagonalization of the Hamiltonian we analyze the ground state and the thermal state of the system in terms of one- and two-particle reduced density matrices. We show how for strong attraction the correlated pairs emerge in the system. We find that the fraction of correlated pairs depends on temperature and we show that this dependence has universal properties analogous to the gap function known from the theory of superconductivity. In contrast to the standard approach based on the variational ansatz and/or perturbation theory, our predictions are exact and are valid also in a strong-attraction limit. Our findings contribute to the understanding of strongly correlated few-body systems and can be verified in current experiments on ultra-cold atoms.