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arXiv:2412.18700

Strong coupling of a chiral molecule with circularly polarised modes inside a cavity

Lara Marie Tomasch, Fabian Spallek, Guido Fuchs, Thomas F. Giesen, Stefan Yoshi Buhmann

Published Dec 24, 2024• 2 citations
arXivHTMLPDF

Abstract

We consider the discriminatory interaction of a chiral molecule with circularly polarised modes inside a cavity. Starting from a generalised Jaynes--Cummings model that includes both electric and magnetic dipole couplings, we derive the Rabi frequency and associated Casimir--Polder potential for a cavity with a single mode of given handedness. One finds that both acquire a discriminatory component whose sign depends on the relative handedness of molecule and cavity mode. We generalise this result to a cavity that supports two modes of different handedness on the basis of superradiant collective field states.

DOI
10.48550/arxiv.2412.18700

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We consider the discriminatory interaction of a chiral molecule with circularly polarised modes inside a cavity. Starting from a generalised Jaynes--Cummings model that includes both electric and magnetic dipole couplings, we derive the Rabi frequency and associated Casimir--Polder potential for a cavity with a single mode of given handedness. One finds that both acquire a discriminatory component whose sign depends on the relative handedness of molecule and cavity mode. We generalise this result to a cavity that supports two modes of different handedness on the basis of superradiant collective field states.
High Resolution Image Download MS PowerPoint Slide Spin-dependent, directional light–matter interactions form the basis of chiral quantum networks. In the solid state, quantum emitters commonly possess circularly polarized optical transitions with spin-dependent handedness. We demonstrate numerically that spin-dependent chiral coupling can be realized by embedding such an emitter in a waveguide-coupled nanocavity, which supports two near-degenerate, orthogonally polarized cavity modes. The chiral behavior arises due to direction-dependent interference between the cavity modes upon coupling to two single-mode output waveguides. Notably, an experimentally realistic cavity design simultaneously supports near-unity chiral contrast, efficient (>95%) cavity-waveguide coupling and enhanced light–matter interaction strength (Purcell factor F P > 70). In combination, these parameters enable the development of highly coherent spin–photon interfaces ready for integration into nanophotonic circuits.
We present a scheme to realize precise discrimination of chiral molecules in a cavity. Assisted by additional laser pulses, cavity fields can evolve into different coherence states with contrary-sign displacements according to the handedness of molecules. Consequently, the handedness of molecules can be read out with homodyne measurement on the cavity, and the successful probability is nearly unity without very strong cavity fields. Numerical results show that the scheme is insensitive to errors, noise, and decoherence. Therefore, the scheme may provide helpful perspectives for accurate discrimination of chiral molecules.
This paper is devoted to a study of a kind of chirality appearing in a model in cavity or circuit quantum electrodynamics. The model especially describes an artificial atom fully coupled to a 1-mode photon in a cavity. This chirality is played in the fully coupled (FC) Hamiltonian by two modified Jaynes-Cummings (JC) Hamiltonians. The modified JC Hamiltonian as well as the standard one has the superradiant ground state energy for sufficiently large coupling strength. The superradiance is caused by a phase transition found by Preparata, called the Dicke-Preparata (DP) superradiance. Using the one common Hamiltonian formalism with the chirality, we theoretically prove the followings: (i) when the coupling strength makes the weak or standard strong coupling regime, the ground state energy of the FC Hamiltonian can be well approximated with that of the standard and modified JC Hamiltonians since the chirality does not work in the regime; (ii) once the coupling strength plunges into the ultra-strong coupling regime, the effect of the chirality is turned on and works in the ground state energy of the FC Hamiltonian. That is, there is a kind of a phase transition concerning the chirality associated with the DP superradiance between the strong coupling regime and the ultra-strong coupling one.
The present work focuses on the strong/weak interaction of many-body spin-systems with a cavity mode. It introduces the necessity of redefining the physical conditions determining the strong/weak coupling regime in those systems. In more complex systems, the effective coupling emerging from the collective dynamics may differ indeed from the actual coupling of each individual subsystem with the bosonic field. This is shown by highlighting some counter-intuitive dynamical effects properly related to the coupling regime: a Jaynes-Cummings dynamics emerging although a strong interaction is present. The universality of this result is demonstrated through the analysis of three distinct systems: a two-qubit, a two-qutrit, and an NNN-qubit chain quantum Rabi models.
We reveal that a chiral cavity distinguishes the resonant and antiresonant interactions between a two-dimensional electron gas and the cavity vacuum. For co-rotating helicities, the modes anticross, exhibiting vacuum Rabi splitting, and retain a bare vacuum ground state. For counter-rotating helicities, the modes cross, acquiring vacuum-mediated energy shifts and a two-mode squeezed ground state. We trace the origin of these observations to the SU(2) and SU(1,1) symmetries of the respective Hamiltonians and present their spectroscopic signatures in chiral photonic crystal cavities. We further predict that cavity chirality produces a handedness-dependent correction to Hall resistivity at finite polariton broadening, while such a correction is not present in an achiral cavity. For the longitudinal resistivity, we find an asymmetric response of the Shubnikov--de Haas oscillations for the different helicities. Finally, we present an experimentally accessible route for detecting the squeezed ground state through current fluctuations. Parameters based on a recently demonstrated terahertz chiral cavity place these effects within experimental reach.