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Dark state number in the Tavis-Cummings model

L. Theerthagiri, Rajesh Narayanan, Ganesh R

Published Jun 30, 2026• 0 citations
Publisher

Abstract

Abstract Quantum mechanics allows for light-matter setups that hold excitations without releasing them as light. Arising from destructive interference processes, they are best seen in a Tavis-Cummings-like setup where two-level atoms (or qubits) are placed within a lossy cavity. If the system is initialized with some qubits excited and some in the ground state, there is a non-zero likelihood of no photons being emitted. This can be framed as a Stern-Gerlach measurement, with a detector to measure if one or more photons leave the cavity. If no photons are detected, the qubits collapse onto a dark state. This can be viewed as heralding of a dark state based on zero photon detection. Building upon this idea, we propose a protocol to measure the number of independent dark states. Remarkably, we show that this quantity is robust to arbitrary levels of disorder in the qubit-photon coupling constants. This provides a rare example of an observable that remains unchanged with any amount of disorder. We then discuss a phase transition where the number of dark states plays the role of an order parameter. This provides a rare example of a phase transition that is completely insensitive to disorder.

DOI
10.21203/rs.3.rs-9754244/v1

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SciPost Physics Core•Jun 16, 2026•0 citations
Abstract Quantum mechanics allows for light-matter setups that hold excitations without releasing them as light. Arising from destructive interference processes, they are best seen in a Tavis-Cummings-like setup where two-level atoms (or qubits) are placed within a lossy cavity. If the system is initialized with some qubits excited and some in the ground state, there is a non-zero likelihood of no photons being emitted. This can be framed as a Stern-Gerlach measurement, with a detector to measure if one or more photons leave the cavity. If no photons are detected, the qubits collapse onto a dark state. This can be viewed as heralding of a dark state based on zero photon detection. Building upon this idea, we propose a protocol to measure the number of independent dark states. Remarkably, we show that this quantity is robust to arbitrary levels of disorder in the qubit-photon coupling constants. This provides a rare example of an observable that remains unchanged with any amount of disorder. We then discuss a phase transition where the number of dark states plays the role of an order parameter. This provides a rare example of a phase transition that is completely insensitive to disorder.
Quantum mechanics allows for light-matter setups that hold excitations without releasing them as light. Arising from destructive interference processes, they are best seen in a Tavis-Cummings-like setup where two-level atoms (or qubits) are placed within a lossy cavity. If the system is initialized with some qubits excited and some in the ground state, there is a non-zero probability that no photons will be emitted. This can be framed as a Stern-Gerlach measurement, with a detector to measure if one or more photons leave the cavity. If no photons are detected, the qubits collapse onto a dark state. This can be viewed as heralding of a dark state based on zero photon detection. Building upon this idea, we propose a protocol to measure the number of independent dark states. Moreover, we show that this quantity is robust to arbitrary levels of disorder in the qubit-photon coupling constants. We then discuss a phase transition where the number of dark states plays the role of an order parameter. This provides an exciting example of a phase transition that is completely insensitive to disorder.
Ensemble of identical two level atoms in dark state neither adsorbs nor emits photons due to destructive interference. It can be used for the source of energy for nano-devices. In Tavis-Cummings cavity the change of light-atom coupling cannot destroy the dark state. We propose the method of dark states preparation based on photon pumping and drain from the optical cavity with two atoms, one from which has Stark or Zeeman splitting of energy levels. This splitting is removed before photon drain from the cavity. The dark state yield after one such cycle has the order of energy level splitting. We show the scheme of the experiment, in which such cycles repeat until the dark state is produced with high probability and the results of computer simulation.
Interference phenomena, such as those observed in Young’s double-slit experiment, are foundational to quantum mechanics, yet their interpretation continues to spark debate. Villas-Boas et al. [Phys. Rev. Lett. 134, 133603 (2025)] propose a quantum-optical framework attributing non-detection in regions of destructive interference to photons occupying ``perfectly dark'' states, which they claim do not interact with a two-level atom sensor due to vanishing coupling in the Jaynes-Cummings Hamiltonian. We argue that this interpretation is fundamentally flawed. Dark states, such as the out-of-phase coherent state ∣α,−α⟩ |\alpha, -\alpha\rangle ∣α,−α⟩, are readily detectable in alternative experimental setups, including dispersive coupling in cavity QED and photon-counting detectors like photomultiplier tubes or avalanche photodiodes, which are sensitive to the photon number operator. This detectability undermines the assertion that dark states are the intrinsic cause of non-detection in destructive interference regions. Instead, the quantum mechanical superposition principle, combined with the Born rule, fully accounts for interference patterns across all detection schemes, as evidenced by well-established experiments such as single-photon double-slit interference, Hong-Ou-Mandel two-photon interference, and cavity QED measurements. By overgeneralizing a detector-specific effect, the dark-state framework introduces an unnecessary and redundant construct, as the standard quantum mechanical formalism already provides a complete and experimentally validated explanation of interference phenomena.
An ensemble of identical two level atoms in dark state neither adsorbs nor emits photons due to destructive interference. Dark states have numerous applications. It can be used for the source of energy for nano-devices; the space of dark states is decoherence free and can serve as the carrier for the fault tolerant quantum computations, etc. Since a dark state does not interact with the electromagnetic field it is an eigenstate of Tavis-Cummings Hamiltonian and the preparation of such states requires the exit from this model. We show how to prepare a dark state by the photon pumping and drain from the optical cavity with two atoms, one from which has Stark or Zeeman splitting of energy levels. This splitting is removed before photon drain from the cavity. The dark state yield after one such cycle has the order of energy level splitting. We show the scheme of the experiment, in which such cycles repeat until the dark state is produced with high probability and the results of its computer simulation. The structure of dark states is briefly discussed.
The collective coupling of an ensemble of molecules to a light field is commonly described by the Tavis-Cummings model. This model includes numerous eigenstates that are optically decoupled from the optically bright polariton states. Accessing these dark states requires breaking the symmetry in the corresponding Hamiltonian. In this paper, we investigate the influence of non-unitary processes on the dark state dynamics in the molecular Tavis-Cummings model. The system is modeled with a Lindblad equation that includes pure dephasing, as it would be caused by weak interactions with an environment, and photon decay. Our simulations show that the rate of pure dephasing, as well as the number of two-level systems, has a significant influence on the dark state population.
Quantum phase transition in Ξ\XiΞ-configuration Tavis-Cummings model driven by an electromagnetic field for a finite number of atoms
The quantum phase transitions of a three-level Tavis-Cummings model in the \Xi Ξ -configuration driven by a single-mode electromagnetic field in a QED cavity are studied for n_a=1,\,2 n a = 1 , 2 , and 4 4 atoms. Although conventional observables like photon number and energy level populations suffice to locate quantum phase transitions, they often lack sensitivity to finite-size effects. Here, we show that the expectation values of the quadratic Casimir invariants associated with the atomic subsystems offer a more robust measure, exhibiting sharp signatures of criticality that are validated by fidelity calculations. Additionally, the von Neumann entropy is employed to map the entanglement landscape between matter and the quantized field. A key finding is that the external driving field acts as a control parameter that shrinks the normal phase region; as the driving intensity increases, the separable ground state vanishes, leading to the dominance of field-matter entanglement across the parameter space.