We predict the generation of noncritically squeezed light through the spontaneous rotational symmetry breaking occurring in a Kerr cavity. The model considers a chi(3)cavity that is pumped by two Gaussian beams of frequencies omega1and omega2. The cavity configuration is such that two signal modes of equal frequency omegas=(omega1+omega2)/2 are generated, these signal fields being first-order Laguerre-Gauss modes. In this system, a spontaneous breaking of the rotational symmetry occurs as the signal field corresponds to a Hermite-Gauss TEM mode. This symmetry breaking leads to the perfect and noncritical (i.e., nondependent on the parameter values) squeezing of the angular momentum of the output TEM mode, which is another TEM mode spatially orthogonal to that in which bright emission occurs.We predict the generation of noncritically squeezed light through the spontaneous rotational symmetry breaking occurring in a Kerr cavity. The model considers a chi(3)cavity that is pumped by two Gaussian beams of frequencies omega1and omega2. The cavity configuration is such that two signal modes of equal frequency omegas=(omega1+omega2)/2 are generated, these signal fields being first-order Laguerre-Gauss modes. In this system, a spontaneous breaking of the rotational symmetry occurs as the signal field corresponds to a Hermite-Gauss TEM mode. This symmetry breaking leads to the perfect and noncritical (i.e., nondependent on the parameter values) squeezing of the angular momentum of the output TEM mode, which is another TEM mode spatially orthogonal to that in which bright emission occurs.

arXiv:0904.1624IEEE Journal of Quantum ElectronicsNov 1, 20099 citations

Stationary squeezed states in two-mode two-boson models

Eugene K. Bashkirov

Optics and SpectroscopyMay 1, 19931 citation

Generalized Squeezing of Boson States

Gerhart Schroff

NATO ASI series. Series B : PhysicsJan 1, 19910 citations

Quantum Squeezing and Sensing with Pseudo-Anti-Parity-Time Symmetry

Xi-Wang Luo, Chuanwei Zhang, Shengwang Du

The emergence of parity-time (PT) symmetry has greatly enriched our study of symmetry-enabled non-Hermitian physics, but the realization of quantum PT symmetry faces an intrinsic issue of unavoidable symmetry-breaking Langevin noises. Here we construct a quantum pseudo-anti-PT (pseudo-APT) symmetry in a two-mode bosonic system without involving Langevin noises. We show that the spontaneous pseudo-APT symmetry breaking leads to an exceptional point, across which there is a transition between different types of quantum squeezing dynamics; i.e., the squeezing factor increases exponentially (oscillates periodically) with time in the pseudo-APT-symmetric (broken) region. Such dramatic changes of squeezing factors and quantum dynamics near the exceptional point are utilized for ultraprecision quantum sensing. These exotic quantum phenomena and sensing applications can be experimentally observed in two physical systems: spontaneous wave mixing nonlinear optics and atomic Bose-Einstein condensates. Our Letter offers a physical platform for investigating exciting APT symmetry physics in the quantum realm, paving the way for exploring fundamental quantum non-Hermitian effects and their quantum technological applications.The emergence of parity-time (PT) symmetry has greatly enriched our study of symmetry-enabled non-Hermitian physics, but the realization of quantum PT symmetry faces an intrinsic issue of unavoidable symmetry-breaking Langevin noises. Here we construct a quantum pseudo-anti-PT (pseudo-APT) symmetry in a two-mode bosonic system without involving Langevin noises. We show that the spontaneous pseudo-APT symmetry breaking leads to an exceptional point, across which there is a transition between different types of quantum squeezing dynamics; i.e., the squeezing factor increases exponentially (oscillates periodically) with time in the pseudo-APT-symmetric (broken) region. Such dramatic changes of squeezing factors and quantum dynamics near the exceptional point are utilized for ultraprecision quantum sensing. These exotic quantum phenomena and sensing applications can be experimentally observed in two physical systems: spontaneous wave mixing nonlinear optics and atomic Bose-Einstein condensates. Our Letter offers a physical platform for investigating exciting APT symmetry physics in the quantum realm, paving the way for exploring fundamental quantum non-Hermitian effects and their quantum technological applications.

arXiv:2108.12873Physical Review LettersApr 29, 202278 citations

Enforced symmetry breaking by invertible topological order

Shang-Qiang Ning, Yang Qi, Zheng‐Cheng Gu +1 more

It is well known that two-dimensional fermionic systems with a nonzero Chern number must break the time-reversal symmetry, manifested by the appearance of chiral edge modes on an open boundary. Such an incompatibility between topology and symmetry can occur more generally. We will refer to this phenomenon as enforced symmetry breaking (ESB) by topological orders. In this work, we systematically study ESB of a finite symmetry group ${G}_{f}$ by fermionic invertible topological orders. Mathematically, the group ${G}_{f}$ is a central extension over a bosonic symmetry group $G$ by the fermion parity group ${\mathbb{Z}}_{2}^{f}$ , characterized by a 2-cocycle $\ensuremath{\lambda}\ensuremath{\in}{\mathcal{H}}^{2}(G,{\mathbb{Z}}_{2})$. For given $G$ and $\ensuremath{\lambda}$, we are able to obtain a series of criteria on the existence or nonexistence of ESB by the corresponding fermionic invertible topological orders. For 2D systems, we define a set of physical quantities to describe symmetry-enriched invertible topological orders and derive obstruction functions using both fermionic and bosonic languages. The study in the bosonic language is performed after gauging the fermion parity, and we find that some obstruction functions are consequences of conditional anomalies of the bosonic symmetry-enriched topological states, with the conditions inherited from the original fermionic system. The obstruction functions are crucial components of the ESB criteria that we derive. With these criteria, we discover many new ESB examples, e.g., we find that the quaternion group ${Q}_{8}$ is incompatible with two copies of $p+ip$ superconductors. We also obtain explicit results on the ESB phenomena of the continuous group ${\mathrm{SU}}_{f}(N)$ by 2D invertible topological orders through a different argument.It is well known that two-dimensional fermionic systems with a nonzero Chern number must break the time-reversal symmetry, manifested by the appearance of chiral edge modes on an open boundary. Such an incompatibility between topology and symmetry can occur more generally. We will refer to this phenomenon as enforced symmetry breaking (ESB) by topological orders. In this work, we systematically study ESB of a finite symmetry group ${G}_{f}$ by fermionic invertible topological orders. Mathematically, the group ${G}_{f}$ is a central extension over a bosonic symmetry group $G$ by the fermion parity group ${\mathbb{Z}}_{2}^{f}$, characterized by a 2-cocycle $\ensuremath{\lambda}\ensuremath{\in}{\mathcal{H}}^{2}(G,{\mathbb{Z}}_{2})$. For given $G$ and $\ensuremath{\lambda}$, we are able to obtain a series of criteria on the existence or nonexistence of ESB by the corresponding fermionic invertible topological orders. For 2D systems, we define a set of physical quantities to describe symmetry-enriched invertible topological orders and derive obstruction functions using both fermionic and bosonic languages. The study in the bosonic language is performed after gauging the fermion parity, and we find that some obstruction functions are consequences of conditional anomalies of the bosonic symmetry-enriched topological states, with the conditions inherited from the original fermionic system. The obstruction functions are crucial components of the ESB criteria that we derive. With these criteria, we discover many new ESB examples, e.g., we find that the quaternion group ${Q}_{8}$ is incompatible with two copies of $p+ip$ superconductors. We also obtain explicit results on the ESB phenomena of the continuous group ${\mathrm{SU}}_{f}(N)$ by 2D invertible topological orders through a different argument.

arXiv:2109.15307Physical Review ResearchJun 6, 20237 citations

Dynamic squeezing in a single-mode boson field interacting with two-level system

Titus Sandu, Viorel Chihaia, W. P. Kirk

Journal of LuminescenceDec 10, 20029 citations

{G}_{f}

by fermionic invertible topological orders. Mathematically, the group

{G}_{f}

is a central extension over a bosonic symmetry group

G

by the fermion parity group

{\mathbb{Z}}_{2}^{f}

, characterized by a 2-cocycle $\ensuremath{\lambda}\ensuremath{\in}{\mathcal{H}}^{2}(G,{\mathbb{Z}}_{2})$. For given

G

and $\ensuremath{\lambda}$, we are able to obtain a series of criteria on the existence or nonexistence of ESB by the corresponding fermionic invertible topological orders. For 2D systems, we define a set of physical quantities to describe symmetry-enriched invertible topological orders and derive obstruction functions using both fermionic and bosonic languages. The study in the bosonic language is performed after gauging the fermion parity, and we find that some obstruction functions are consequences of conditional anomalies of the bosonic symmetry-enriched topological states, with the conditions inherited from the original fermionic system. The obstruction functions are crucial components of the ESB criteria that we derive. With these criteria, we discover many new ESB examples, e.g., we find that the quaternion group

{Q}_{8}

is incompatible with two copies of

p+ip

superconductors. We also obtain explicit results on the ESB phenomena of the continuous group

{\mathrm{SU}}_{f}(N)

by 2D invertible topological orders through a different argument.