Broken symmetries and the generation of classical observables in large systems

We propose a novel method to generate non-classical states of a single-mode microwave field, and to produce macroscopic cat states by virtue of a three-level system with $Δ$ -shaped (or cyclic) transitions. This exotic system can be implemented by a superconducting quantum circuit with a broken symmetry in its effective potential. Using the cyclic population transfer, controllable single-mode photon states can be created in the third transition when two classical fields are applied to induce the other two transitions. This is because, for large detuning, two classical fields are equivalent to an effective external force, which derives the quantized single mode. Our approach is valid not only for superconducting quantum circuits but also for any three-level quantum system with $Δ$ -shaped transitionsWe propose a novel method to generate non-classical states of a single-mode microwave field, and to produce macroscopic cat states by virtue of a three-level system with $Δ$-shaped (or cyclic) transitions. This exotic system can be implemented by a superconducting quantum circuit with a broken symmetry in its effective potential. Using the cyclic population transfer, controllable single-mode photon states can be created in the third transition when two classical fields are applied to induce the other two transitions. This is because, for large detuning, two classical fields are equivalent to an effective external force, which derives the quantized single mode. Our approach is valid not only for superconducting quantum circuits but also for any three-level quantum system with $Δ$-shaped transitions

arXiv:quant-ph/0506011Jun 1, 20055 citations

Spontaneous Symmetry Breaking and Phase Coherence of a Photon Bose-Einstein Condensate Coupled to a Reservoir

Julian Schmitt, Tobias Damm, David Dung +4 more

We examine the phase evolution of a Bose-Einstein condensate of photons generated in a dye microcavity by temporal interference with a phase reference. The photoexcitable dye molecules constitute a reservoir of variable size for the condensate particles, allowing for grand canonical statistics with photon bunching, as in a lamp-type source. We directly observe phase jumps of the condensate associated with the large statistical number fluctuations and find a separation of correlation time scales. For large systems, our data reveal phase coherence and a spontaneously broken symmetry, despite the statistical fluctuations.We examine the phase evolution of a Bose-Einstein condensate of photons generated in a dye microcavity by temporal interference with a phase reference. The photoexcitable dye molecules constitute a reservoir of variable size for the condensate particles, allowing for grand canonical statistics with photon bunching, as in a lamp-type source. We directly observe phase jumps of the condensate associated with the large statistical number fluctuations and find a separation of correlation time scales. For large systems, our data reveal phase coherence and a spontaneously broken symmetry, despite the statistical fluctuations.

arXiv:1512.07148Physical Review LettersJan 22, 201650 citations

Space–Time Symmetries and Classical Observables

UMBERTO LOMBARDO, G. Giuliani, Yifei Niu

UNITEXT for physicsJan 1, 20240 citations

60 YEARS OF BROKEN SYMMETRIES IN QUANTUM PHYSICS

DMITRY V. SHIRKOV

Lomonosov Conference on Elementary Particle PhysicsOct 1, 20103 citations

Cumulants of time-integrated observables of closed quantum systems and PT symmetry with an application to the quantum Ising chain

James M. Hickey, Emanuele Levi, Juan P. Garrahan

We study the connection between the cumulants of a time-integrated observable of a quantum system and the $\mathcal{P}\mathcal{T}$ -symmetry properties of the non-Hermitian deformation of the Hamiltonian from which the generating function of these cumulants is obtained. This non-Hermitian Hamiltonian can display regimes of broken and of unbroken $\mathcal{P}\mathcal{T}$ symmetry, depending on the parameters of the problem and on the counting field that sets the strength of the non-Hermitian perturbation. This in turn determines the analytic structure of the long-time cumulant generating function (CGF) for the time-integrated observable. We consider in particular the case of the time-integrated (longitudinal) magnetization in the one-dimensional Ising model in a transverse field. We show that its long-time CGF is singular on a curve in the magnetic field/counting field plane that delimits a regime where $\mathcal{P}\mathcal{T}$ symmetry is spontaneously broken (which includes the static ferromagnetic phase), from one where it is preserved (which includes the static paramagnetic phase). In the paramagnetic phase, conservation of $\mathcal{P}\mathcal{T}$ symmetry implies that all cumulants are sublinear in time, a behavior usually associated with the absence of decorrelation.We study the connection between the cumulants of a time-integrated observable of a quantum system and the $\mathcal{P}\mathcal{T}$-symmetry properties of the non-Hermitian deformation of the Hamiltonian from which the generating function of these cumulants is obtained. This non-Hermitian Hamiltonian can display regimes of broken and of unbroken $\mathcal{P}\mathcal{T}$ symmetry, depending on the parameters of the problem and on the counting field that sets the strength of the non-Hermitian perturbation. This in turn determines the analytic structure of the long-time cumulant generating function (CGF) for the time-integrated observable. We consider in particular the case of the time-integrated (longitudinal) magnetization in the one-dimensional Ising model in a transverse field. We show that its long-time CGF is singular on a curve in the magnetic field/counting field plane that delimits a regime where $\mathcal{P}\mathcal{T}$ symmetry is spontaneously broken (which includes the static ferromagnetic phase), from one where it is preserved (which includes the static paramagnetic phase). In the paramagnetic phase, conservation of $\mathcal{P}\mathcal{T}$ symmetry implies that all cumulants are sublinear in time, a behavior usually associated with the absence of decorrelation.

arXiv:1403.4538Physical Review BSep 2, 20144 citations

We propose a novel method to generate non-classical states of a single-mode microwave field, and to produce macroscopic cat states by virtue of a three-level system with

Δ

-shaped (or cyclic) transitions. This exotic system can be implemented by a superconducting quantum circuit with a broken symmetry in its effective potential. Using the cyclic population transfer, controllable single-mode photon states can be created in the third transition when two classical fields are applied to induce the other two transitions. This is because, for large detuning, two classical fields are equivalent to an effective external force, which derives the quantized single mode. Our approach is valid not only for superconducting quantum circuits but also for any three-level quantum system with

Δ

-shaped transitions

We study the connection between the cumulants of a time-integrated observable of a quantum system and the

\mathcal{P}\mathcal{T}

-symmetry properties of the non-Hermitian deformation of the Hamiltonian from which the generating function of these cumulants is obtained. This non-Hermitian Hamiltonian can display regimes of broken and of unbroken

\mathcal{P}\mathcal{T}

symmetry, depending on the parameters of the problem and on the counting field that sets the strength of the non-Hermitian perturbation. This in turn determines the analytic structure of the long-time cumulant generating function (CGF) for the time-integrated observable. We consider in particular the case of the time-integrated (longitudinal) magnetization in the one-dimensional Ising model in a transverse field. We show that its long-time CGF is singular on a curve in the magnetic field/counting field plane that delimits a regime where

\mathcal{P}\mathcal{T}

symmetry is spontaneously broken (which includes the static ferromagnetic phase), from one where it is preserved (which includes the static paramagnetic phase). In the paramagnetic phase, conservation of

\mathcal{P}\mathcal{T}

symmetry implies that all cumulants are sublinear in time, a behavior usually associated with the absence of decorrelation.