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arXiv:2302.07163 · Physical Review A

Switchable superradiant phase transition with Kerr magnons

Gang Liu, Wei Xiong, Zu‐Jian Ying

Published Sep 7, 2023• 37 citations
arXivHTMLPDF

Abstract

The superradiant phase transition (SPT) has been widely studied in cavity quantum electrodynamics (CQED). However, this SPT is still subject to ongoing debates due to the no-go theorem induced by the so-called ${\mathbf{A}}^{2}$ term (AT). We propose a hybrid quantum system, consisting of a single-mode cavity simultaneously coupled to both a two-level system and yttrium-iron-garnet sphere supporting magnons with Kerr nonlinearity, to restore the SPT against the AT. The Kerr magnons here can effectively introduce an additional AT tunable and strong enough to counteract the intrinsic AT, via adiabatically eliminating the degrees of freedom of the magnons. We show that the Kerr-magnon-induced SPT can exist in both cases of ignoring and including the intrinsic AT. Without the intrinsic AT, the critical coupling strength can be dramatically reduced by introducing the Kerr magnons, which greatly relaxes the experimental conditions for observing the SPT. With the intrinsic AT, the forbidden SPT can be recovered with the Kerr magnons in a reversed way. Our work paves a potential way to manipulate the SPT against the AT in hybrid systems combining CQED and nonlinear magnonics.

DOI
10.1103/physreva.108.033704

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The superradiant phase transition (SPT) has been widely studied in cavity quantum electrodynamics (CQED). However, this SPT is still subject to ongoing debates due to the no-go theorem induced by the so-called A2{\mathbf{A}}^{2}A2 term (AT). We propose a hybrid quantum system, consisting of a single-mode cavity simultaneously coupled to both a two-level system and yttrium-iron-garnet sphere supporting magnons with Kerr nonlinearity, to restore the SPT against the AT. The Kerr magnons here can effectively introduce an additional AT tunable and strong enough to counteract the intrinsic AT, via adiabatically eliminating the degrees of freedom of the magnons. We show that the Kerr-magnon-induced SPT can exist in both cases of ignoring and including the intrinsic AT. Without the intrinsic AT, the critical coupling strength can be dramatically reduced by introducing the Kerr magnons, which greatly relaxes the experimental conditions for observing the SPT. With the intrinsic AT, the forbidden SPT can be recovered with the Kerr magnons in a reversed way. Our work paves a potential way to manipulate the SPT against the AT in hybrid systems combining CQED and nonlinear magnonics.
The A2{\mathbf{A}}^{2}A2 term presents a fundamental challenge to realizing the superradiant phase transition (SPT) in cavity quantum electrodynamics. Here, we propose a hybrid quantum system enabling SPT regardless of the presence of the A2{\mathbf{A}}^{2}A2 term. The system consists of a qubit, a mechanical mode, and an optical cavity, where the qubit and mechanical mode constitute a quantum Rabi model, while the mechanical mode and cavity form an optomechanical system. Crucially, the auxiliary cavity introduces a switchable A2{\mathbf{A}}^{2}A2 term that effectively counteracts or even fully eliminates the original A2{\mathbf{A}}^{2}A2 effect. This allows controllable observation of SPT, diagnosed via the second-order equal-time correlation function g(2)(0){g}^{(2)}(0)g(2)(0) of phonons. Furthermore, the auxiliary cavity exponentially reduces the critical coupling strength, significantly relaxing experimental requirements. In addition, we show that phonons in the normal phase display bunching but are coherent in the superradiant phase. Interestingly, higher-order squeezing is found in both phases, with near-perfect higher-order squeezing achieved at the SPT point, establishing it as a probe for SPT behavior. Our work demonstrates that hybridizing optomechanics and cavity quantum electrodynamics provides a promising route to accessing SPT physics in the presence of the A2{\mathbf{A}}^{2}A2 term.
We propose a scheme to engineer the superradiant phase transition (SPT) in cavity magnonics by periodically modulating the frequency of the magnon mode. The studied system is composed of a yttrium iron garnet (YIG) sphere positioned inside a microwave cavity, where magnons in the YIG sphere are strongly coupled to microwave photons. Under the Floquet drive, the effective frequencies of both the cavity and magnon modes can be readily controlled via the frequency and strength of Floquet field. This tunability allows the cavity magnonic system to support a rich steady-state phase diagram, featuring parity-symmetric, parity-symmetry-broken, bistable, and unstable phases. With the increase of Floquet-field strength, the system exhibit a discontinuous phase transition from the parity-symmetric phase to the parity-symmetry-broken phase at a critical threshold, accompanied by an abrupt jump of the magnon occupation from zero to a finite value. Upon further increase of Floquet-field strength, the magnon occupation declines continuously from a nonzero value back to zero, corresponding to a second-order phase transition that restores the parity-symmetric phase. Additionally, fluctuations in magnon number during the SPT process are examined. Our work establishes an alternative route to engineer the cavity-magnon SPT without relying on microwave parametric drive.
A2\bf A^2A2-robust superradiant phase transition in hybrid qubit-cavity optomechanics
The A2\mathbf{A}^2A2 term presents a fundamental challenge to realizing the superradiant phase transition (SPT) in cavity quantum electrodynamics. Here, we propose a hybrid quantum system enabling SPT regardless of the presence of the A2\mathbf{A}^2A2 term. The system consist of a qubit, a mechanical mode, and an optical cavity, where the qubit and mechanical mode constitute a quantum Rabi model, while the mechanical mode and cavity form an optomechanical system. Crucially, the auxiliary cavity introduces a switchable A2\mathbf{A}^2A2 term that effectively counteracts or even fully eliminates the original A2\mathbf{A}^2A2 effect. This allows controllable observation of SPT, diagnosed via the second-order equal-time correlation function g(2)(0)g^{(2)}(0)g(2)(0) of phonons. Furthermore, the auxiliary cavity exponentially reduces the critical coupling strength, significantly relaxing experimental requirements. In addition, we show that phonons in the normal phase display bunching, but coherent in the superradiant phase. Interestingly, higher-order squeezing is found in both phases, with near-perfect higher-order squeezing achieved at the SPT point, establishing it as a probe for SPT behavior. Our work demonstrates that hybridizing optomechanics and cavity quantum electrodynamics provides a promising route to accessing SPT physics in the presence of the A2\mathbf{A}^2A2 term.
We theoretically study the superradiant phase transition (SPT) in an indirect Rabi model, where both a two-level system and a single-mode bosonic field couple to an auxiliary bosonic field. We find that the indirect spin-field coupling induced by the virtual excitation of the auxiliary field can allow the occurrence of a SPT at a critical point, and the influence of the so-called A2{A}^{2}A2 term in the normal Rabi model is naturally avoided. In the large detuning regime, we present the analytical expression of quantum critical point in terms of the original system parameters. The critical atom-field coupling strength is tunable, which will loosen the conditions on realizing the SPT. Considering a hybrid magnon-cavity-qubit system, we predict the squeezed cat state of magnon generated with feasible experimental parameters, which has potential applications in quantum metrology and quantum information processing.
Abstract The superradiant phase transition in thermal equilibrium is a fundamental concept bridging statistical physics and electrodynamics, which has never been observed in real physical systems since the first proposal in the 1970s. The existence of this phase transition in cavity quantum electrodynamics systems is still subject of ongoing debates due to the no-go theorem induced by the so-called A2 term. Moreover, experimental conditions to study this phase transition are hard to achieve with current accessible technology. Based on the platform of nuclear magnetic resonance, here we experimentally simulate the occurrence of an equilibrium superradiant phase transition beyond no-go theorem by introducing the antisqueezing effect. The mechanism relies on that the antisqueezing effect recovers the singularity of the ground state via exponentially enhancing the zero point fluctuation of system. The strongly entangled and squeezed Schrödinger cat states of spins are achieved experimentally in the superradiant phase, which may play an important role in fundamental tests of quantum theory and implementations of quantum metrology.
Hybrid quantum systems have attracted much attention due to the fact that they combine the advantages of different physical subsystems. Cavity QED (cavity quantum electrodynamics) with magnons is a hybrid quantum systems that combines a YIG (Yttrium Iron Garnet) sphere and a 3D (three-dimensional) rectangular microwave cavity. Based on this hybrid photon-magnon system, we obtain an approximate analytic solution by the RWA (rotating wave approximation) with an ingenious transformation. After skillfully diagonalizing the Hamiltonian, we show that the Kerr-nonlinearity interactions could yield a negativity value of the Wigner function, periodic quadrature squeezing effects, antibunching property, and field nonclassicality in the magnon. Our work may stimulate the study of nonclassicality of photon-magnon coupling systems and its potential applications in quantum information processing.