The Study Of Higher-order Squeezing Based On Dissipation Effect Of Atomic Reservoir

Squeezing is one of the key subjects in quantum optics,laser physics and nonlinear op-tics,and finds wide applications in high-precision measurements.Squeezing of an optical field is defined when quantum fluctuations in one quadrature are reduced below what is for the minimum uncertainty state and the quantum fluctuations in the conjugate quadra-ture are enhanced.Therein,Higher-order squeezed and entangled states are important resources for universal quantum computation and entanglement distillation because it can improve the efficiency of quantum information tasks.Due to either coherent or dissipa-tive interactions with the atoms,the evolutions of the Bogoliubov modes towards the vacuum states have been shown to lead to second-order squeezing of the involved optical fields.However,there has been no report so far that shows any relation of the reservoir engineering to higher-order squeezing.Our motivation is to fill in gaps in this aspect.Here we push the dissipative interactions towards higher-order squeezing,which is not simply determined by second-order squeezing but instead by different criteria involving higher-order moments.On the one hand,we put the Bogoliubov modes of the coherent population trapping(CPT)-based atomic reservoir dissipate completely to the vacuum s-tates and then yields almost perfect fourth-order squeezing(90%?100%).On the other hand,We try to add a two-level ensemble to make up for the missing dissipative channel of one two-level ensemble.We present a scheme of two two-level atomic ensembles on generating higher-order squeezing of a two-mode optical field.First,we have presented a CPT-based scheme for higher-order squeezing of two op-tical fields.This scheme is robust against the spontaneous emission and experimental-ly more accessible in a realistic atomic or molecular system because the intrinsic two-photon processes are induced by the dressing fields between the atomic ground states.In this paper,a good higher-order squeezing conditions are given in detail,respectively.(?)>>1 or sinh(2r>>1;(?).Al>>?l,cosh2 r;(?)Rl=(Al-Bl)sinh(2r)>>Bl.The condition(?)defines a possible large squeezing,the condition(?)supports the dom-inance of the induced interactions over the environmental damping,and the condition(?)represents a good compatibility of a large squeezing parameter with the dominant induced dissipation.Now the key of the problem turns to whether we can find a real-istic atomic or molecular system in which the conditions(?-?)are well satisfied,then a comparison between CPT and two-level atoms that satisfies the condition.The present mechanism is robust against spontaneous emission since the atoms stay largely in the ground states.The squeezing is based on dissipative effects of Bogoliubov modes that are formed from two original fields through a squeezing parameter r.Whether the squeezing degree,defined by r,is reached depends on whether the net dissipation rate ?A is enough to support a considerable compatibility parameter R=?A sinh(2r).As the common fea-ture of the two representative reservoirs,an opposite change happens in sinh(2r)and?A as a system-dependent nonlinear function x tends towards zero.While the squeezing parameter rises in a reversely proportional form sinh(2r)(?)1/x??,the net dissipation rate tends towards zero ?A?0.The CPT-based reservoir has an x-linear dependence?A(?)x?C for two dissipative channels(C is a cooperativity parameter and ?is a cavity loss rate),and sustains R(?)?C,which is large enough to preserve almost ideal fourth-order squeezing.In sharp contrast,the two-level reservoir takes an x-square dependence?A(?)x2?C for one dissipative channel,and gives rise to R(?)x?C?0 and to a limited squeezing.Second,we propose to use two near-resonantly dressed atoms as a dissipation reser-voir to generate higher-order two-mode squeezing.The higher-order squeezing can be enhanced in comparison with one two-level atomic reservoir.This is essentially attribut-ed to one more Bogoliubov mode produced by the dressing field induced nonlinearities.The common dissipation evolution of two Bogoliubov modes towards their own vacu-um states leads to the enhanced higher-order squeezing of the involved optical fields.The squeezing parameter and the net dissipative rates,which are two decisive factors for quan-tum correlations,are strongly reversely dependent on the atom-field detunings.Optimal squeezing appears in the intermediate regime,where the squeezing parameter and the dissipation rates are both considerably large.Usually it is expected that the higher-order squeezing is generated from parametric processes,just as for the squeezing in quadra-tures.But our scheme is generated by the engineered dissipative processes.On resonance or close to resonance,resonant absorption of atoms are accompanied with spontaneous emission,which spoils any possibly existent squeezing of the coupled optical fields.In order to overcome this obstacle,one has to work in the far-off-resonance regimes,where the atoms stay dominantly in the ground state and then there is no longer spontaneous emission,and at the same time,the dispersive interactions dominate over the absorptive interactions.we find that:First,the near-resonant atom-field interactions can be used to generate higher-order two-mode squeezing of quantum fluctuations.This is in sharp contrast to the dispersive interaction.Simultaneous dissipation of two Bogoliubov modes towards its own vacuum steady states can enhance higher-order squeezing comparing to the case of only one Bogoliubov mode.In addition,the asymmetry of the dissipation channels and the mismatching of the phase between the two dissipation channels can spoil the squeezing degree significantly.Thirdly,physically,optimal squeezing appears in the intermediate regime of the normalized detuning where the squeezing parameter and the dissipation rates are both considerably large for the Bogoliubov modes.Because only squeezing defined by the intermediate value of the squeezing parameter is preserved through the dominance of the engineered dissipation over the vacuum dissipation,the achievable squeezing is limited to a certain degree.