Noncritical generation of nonclassical frequency combs via spontaneous rotational symmetry breaking

Abstract

Synchronously pumped optical parametric oscillators (SPOPOs) are optical cavities containing a nonlinear crystal capable of down-converting a frequency comb to lower frequencies. These have received a lot of attention lately, because their intrinsic multimode nature makes them compact sources of quantum correlated light with promising applications in modern quantum information technologies. In this work we show that SPOPOs are also capable of accessing the challenging but interesting regime where spontaneous symmetry breaking plays a crucial role in the quantum properties of the emitted light, difficult to access with any other nonlinear optical cavity. Apart from opening the possibility of studying experimentally this elusive regime of dissipative phase transitions, our predictions will have a practical impact, since we show that spontaneous symmetry breaking provides a specific spatiotemporal mode with perfect squeezing for any value of the system parameters, turning SPOPOs into robust sources of highly nonclassical light above threshold. Introduction.-To date, optical parametric oscillators (OPOs) constitute the main source of nonclassical states of light, finding numerous applications in emerging quantum technologies, e.g. in the fields of quantum metrology [1][2][3][4][5][6][7][8][9] or quantum information with continuous variables [10][11][12]. OPOs are optical cavities containing nonlinear crystals supporting the so-called parametric down conversion (PDC) process, by means of which a pump photon of frequency ω p is converted into a pair of photons of frequencies ω s and ω i (socalled, arbitrarily in the OPO case, signal and idler), and vice-versa, with ω s + ω i = ω p [13,14]. This generates strong quantum correlations between signal and idler (e.g. twin beams [15,16]) The PDC Hamiltonian reads χ p,s,i f p,s,iâpâ

Modes and states in Quantum Optics

“…Above threshold and in the case of degenerate T EM 01 and T EM 10 spatial modes, the SPOPO is predicted to generate bright light in a non-classical state (Navarrete-Benlloch et al, 2017), because of a symmetry-breaking effect between the transverse modes.…”

Pattern formation and exotic order in driven-dissipative Bose-Hubbard systems

“…We can analyze the stability of these striped density waves by particularizing Eqs. (15) to the solution of Eqs. (16) and (19).…”

“…A profound question is then how to generalize these ideas to non-equilibrium quantum systems, where the interplay between the intrinsic quantum fluctuations and external non-equilibrium conditions might give rise to richer phenomena than what is expected on the basis of these effects separately. A recent example of this is the dissipative generation of nonclassical states via spontaneous symmetry breaking in quantum optical systems [11][12][13][14][15]. The situation is further complicated and potentially richer when the quantum system is an interacting many-body system, opening avenues for observ-ing exotic quantum states of matter that are absent in either its equilibrium quantum counterparts or in nonequilibrium classical systems.…”

Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation

“…When such functions are chosen as K mα (t) and K nβ (t ), respectively, and summing over α and β, one can compute spectral densities corresponding to the correlations X mn (t, t ), see (16). The choice P α (t) = P β (t ) = 1 is also interesting as it provides the spectral densities corresponding to the elementary correlations C αβ (t, t ), which in some cases are proportional to measurable quadratures [88][89][90][91][92]. Finally, when r is formed of annihilation and creation operators, with the choice P α (t) = Λ α (t)K mα (t) and P β (t ) = Λ β (t )K nβ (t ), (24) allows the computation of spectral densities corresponding to homodyne-detection experiments when the local oscillator is a T -periodic function [100], in which case Λ α (t) and Λ β (t ) are proportional to the amplitude (or its complex conjugate) of that local oscillator.…”

“…Due to the generally nonlinear nature of such equations, exact solutions are hard or impossible to find, except for very specific cases. Analytic or semi-analytic insight is usually gained by using the so-called standard linearization technique, which typically provides sensible results, except close to phase transitions or in the presence of spontaneous symmetry breaking, which nevertheless can be treated with suitable generalizations of such technique [50,[88][89][90][91][92][93][94]. Within this approach, one considers small quantum fluctuations around a reference classical state, leading to a linear system of Langevin equations for the fluctuations, which is easily handled only if the classical reference is time independent.…”