Quantum entanglement and squeezing in coupled harmonic and anharmonic oscillator systems

We investigate the fundamental connection between quadrature squeezing and continuous variable entanglement within a general class of two-coupled oscillator systems. We determine the quantitative relationship between them through the squeezing parameter and the entanglement entropy of the lowest energy eigenstate of the coupled oscillator systems numerically. Unlike the relation between entanglement and uncertainty product, we found that this relationship is, by no means, the same for the whole class of coupled oscillator systems: to a large extent it depends on the order and strength of the anharmonic potential, which implies that knowledge of the anharmonic potential of the coupled oscillator system is required before one can characterize the degree of entanglement through the squeezing parameter. Our results reveal that a more effective approach to enhance squeezing is to adjust the anharmonicity of the system potential, instead of increasing the quantum correlations between the oscillators. In addition, by probing into a quantum catastrophe model, we uncover transitions in the entanglement entropy and squeezing relation as the potential changes from a single well to a triple well, and then a double-well structure. The transitions appear through distinct entropy–squeezing relation, with a multi-well structure displaying a larger change in the antisqueezing behavior of the position quadrature than the single-well structure, for the same change in the entanglement entropy.     

Time-resolved entanglement and photon number correlation of twin beams: Application to quantum key distribution scheme

Quantum entanglement and intensity correlations in continuous variable (CV) regimes have investigated in the time domain in addition to many analogous investigations performed in the frequency domain. The specific signatures of time-resolved CV quadrature entanglement and intensity difference squeezing have been analyzed for periodically-pulsed optical parametric oscillator (OPO). An application to quantum key distribution scheme based on intensity correlation of twin beams has also been considered. The text was submitted by the author in English.     

Non-classical radiation emission by a coherent conductor

We report experimental evidence that the microwave electromagnetic field generated by a normal conductor, here a tunnel junction placed at ultra-low temperature, can be non-classical. By measuring the quadratures of the electromagnetic field at one or two frequencies in the GHz range, we demonstrate the existence of squeezing as well as entanglement in such radiation. In one experiment, we observe that the variance of one quadrature of the photo-assisted noise generated by the junction goes below its vacuum level. In the second experiment, we demonstrate the existence of correlations between the quadratures taken at two frequencies, which can be stronger than allowed by classical mechanics, proving that the radiation at those two frequencies are entangled.¹     

Superfluidity and collective oscillations of trapped Bose-Einstein condensates in a periodical potential

Quadrature squeezed cylindrically polarized modes contain entanglement not only in the polarization and spatial electric field variables but also between these two degrees of freedom [C. Gabriel et al., Phys. Rev. Lett. 106, 060502 (2011)]. In this paper we present tools to generate and detect this entanglement. Experimentally we demonstrate the generation of quadrature squeezing in cylindrically polarized modes by mode transforming a squeezed Gaussian mode. Specifically, ?1.2 dB ± 0.1 dB of amplitude squeezing are achieved in the radially and azimuthally polarized mode. Furthermore, theoretically it is shown how the entanglement contained within these modes can be measured and how strong the quantum correlations are, depending on the measurement scheme.     

Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes

Quantum systems such as, for example, photons, atoms, or Bose-Einstein condensates, prepared in complex states where entanglement between distinct degrees of freedom is present, may display several intriguing features. In this Letter we introduce the concept of such complex quantum states for intense beams of light by exploiting the properties of cylindrically polarized modes. We show that already in a classical picture the spatial and polarization field variables of these modes cannot be factorized. Theoretically it is proven that by quadrature squeezing cylindrically polarized modes one generates entanglement between these two different degrees of freedom. Experimentally we demonstrate amplitude squeezing of an azimuthally polarized mode by exploiting the nonlinear Kerr effect in a specially tailored photonic crystal fiber. These results display that such novel continuous-variable entangled systems can, in principle, be realized.     

在两个耦合的量子点和腔QED系统中的双模激子的压缩性质(英文)

本文研究了在两个耦合的量子点和腔QED系统中的双模激子的压缩性质.讨论了不同的初始光场对双模激子的正常压缩与和压缩的影响.计算表明,当初始态光场制备在相干态时,双模激子既不存在正常压缩,也不存在和压缩,这说明双模激子振辐的两个正交分量具有相同的量子涨落;然而,当初始腔场处于压缩真空态时,无论是正常压缩还是和压缩,双模激子振辐的两个正交分量总有一个存在压缩.这意味着量子噪声能被有效的得到抑制.此外,两种情形下的最大压缩都由初始腔场的压缩因子r决定.经过比较,我们还发现双模激子的正常压缩比和压缩大.     

Impact of quantum–classical correspondence on entanglement enhancement by single-mode squeezing

Quantum entanglement between two field modes can be achieved through the collective squeezing of the two respective modes. If single-mode squeezing is performed prior to such a two-mode squeezing, an enhancement of entanglement production can happen. Interestingly, the occurrence of this enhancement can be implicitly linked to the local classical dynamical behavior via the paradigm of quantum–classical correspondence. In particular, the entanglement generated through quantum chaos is found to be hardly enhanced by prior squeezing, since it is bounded by the saturation value of the maximally entangled Schmidt state with fixed energy. These results illustrate that entanglement enhancement via initial squeezing can serve as a useful indicator of quantum chaotic behaviour.     

Phase-modulated quadrature squeezing in two coupled cavities containing a two-level system

The phase-modulated quadrature squeezing in the system that composed of two coupled cavities interacting with a two-level atom is investigated. The variances of the amplitude and phase quadrature of the output field are calculated.It turns out that the squeezing behaviors of the output field can be obviously modified due to the phase difference of the coupling strengths between the atom and the two cavities. The squeezing in one quadrature(i.e., phase quadrature) can be transferred into another(i.e., amplitude quadrature), or the quadrature squeezing located at the low-frequency region can be transferred into the high-frequency region by modulating the relative phase of the coupling strengths. Furthermore, the effects of the decay mismatch between the two cavities and the coupling mismatch between the atom and the cavities on the quadrature squeezing have been discussed. The results show that both the decay mismatch and the coupling mismatch play a positive role in generating better quadrature squeezing.     

Single-atom entropy squeezing and quantum entanglement in Tavis--Cummings model with atomic motion

We examine the single-atom entropy squeezing and the atom-field entanglement in a system of two moving twolevel atoms interacting with a single-mode coherent field in a lossless resonant cavity.Our numerical calculations indicate that the squeezing period,the squeezing time and the maximal squeezing can be controlled by appropriately choosing the atomic motion and the field-mode structure.The atomic motion leads to a periodical time evolution of entanglement between the two-atom and the field.Moreover,there exists corresponding relation between the time evolution properties of the atomic entropy squeezing and that of the entanglement between the two atoms and the field.     

单-双模组合压缩热态的纠缠性质及在量子隐形传态中的应用

基于单-双模组合压缩真空态一定范围内能够获得压缩增强的效果,引入单-双模组合压缩热态(DSMST),讨论其纠缠性质.利用Weyl编序算符在相似变换下的不变性,简洁方便地导出了DSMST的纠缠度-负对数值,并给出了当热效应存在时保持纠缠的条件.研究表明:与通常的双模压缩态相比,随着参数的增加,DSMST的纠缠度增加.作为DSMST的应用,利用其实现相干态的量子隐形传输.结果表明:不同于纠缠度随压缩参数增加,保真度获得改善是有条件的,该条件恰好就是一正交分量涨落出现压缩增强的参数区域.此外,解析推导了有效隐形传输保真度(1/2)的条件.     

纠缠双原子对场熵压缩特性的影响

研究了相干态光场与纠缠双原子相互作用系统中场熵的压缩性质,借助于数值计算,讨论了双原子纠缠度及光场强度对场熵压缩的影响。所得结果表明,双原子初态的纠缠度对压缩的持续时间和压缩深度具有决定性的影响。当双原子初始时刻处于最大纠缠态时,场熵具有较大的压缩深度和较长的压缩时间。初始光场强度对场熵的压缩深度和压缩时间也具有显著的影响。光场愈弱,场熵的压缩性愈好。     

Cavity-Induced Enhancement of Squeezing in Resonance Fluorescence of a V-Type Three-Level Atom

The quadrature squeezing spectra in the resonance fluorescence of a V-type three-level atom driven by a coherent field and coupled to a single-mode cavity is investigated. For weak excitation, the fluorescence field exhibit squeezing in the out-of-phase quadrature. The coupling between the atom and the cavity mode can greatly enhance the squeezing centred at the laser frequency. More importantly, for strong excitation, under the effect of the cavity-atom coupling, the in-phase quadrature of fluorescence can exhibit two-mode squeezing at the two inner sideband frequencies. By working in the dressed-state representation and hiring secular approximation, we give an analytical explanation for the effect. The result shows, under appropriate conditions, the squeezing can be greatly enhanced by appropriately tuning the cavity resonant frequency.     

Entropy squeezing of multi-photon field interacting with a single Cooper-pair box

We investigate the entropy squeezing and entanglement of the Cooper-pair box interacting with multi-photon cavity field. The field is prepared initially in the coherent state, while the Cooper-pair box is assumed to start from a mixed state. We find that the number of photons and the detuning parameters play an important role in the entropy squeezing and entanglement. We observe that the entropy squeezing can be used as a good indicator of the entanglement. This study opens promising perspectives for creating remote quantum information processing networks.     

量子干涉效应对原子共振荧光非经典特性的影响

研究了两个自发辐射路径之间的量子干涉效应对V型三能级原子压缩谱和光子反聚束效应的影响 .结果表明 ,量子干涉可以加强压缩效应和展宽出现压缩的相位角分量的范围 ,但却会减弱反聚束效应.Phase-dependent squeezing spectrum and photon antibunching of resonance fluorescence from a three-level V-type atom driven by a coherent field are investigated. We show that for weak excitation intensities quantum interference can greatly enhance squeezing and change the phase quadrature at which the maximum squeezing occurs. We also notice that the maximum squeezing can appear not only in either the in-phase or the out-of-phase quadrature but also in any phase quadrature, and at which phase quadrature...     

V型三能级原子与非经典光场作用中光场特性的变化

研究了V型三能级原子BEC与双模压缩光场相互作用系统中,忽略原子间相互作用和考虑原子间相互作用时光场的正交压缩和光子数压缩。结果表明,光场的正交压缩依赖于压缩参数,而光子数压缩与压缩参数、光场信号强度有关,在一定条件下,两种压缩可同时存在。原子间相互作用影响两种压缩的涨落随时间变化的周期,以及正交分量涨落随时间变化的幅度,而对光子数压缩涨落随时间变化的幅度几乎无影响。     

Enhanced squeezing and entanglement in a non-degenerate three-level cascade laser with injected squeezed light

We consider a non-degenerate three-level cascade laser coupled to a two-mode squeezed vacuum reservoir via the lossy single-port mirror. Applying the pertinent master equation, we analyze the effects of the injected squeezed light on the quadrature squeezing, entanglement and normalized intensity difference fluctuations. We show that the injected squeezed light considerably enhances the degree of squeezing and entanglement in the two-mode light for certain initial conditions. Moreover, the injected squeezed light increases the mean photon number where the squeezing and entanglement is significant. We also show that the presence of the injected squeezed light greatly reduces the noise in the intensity difference.     

Continuous-Variable Entanglement Generation from a Four-State Atom under Raman Excitation

We investigate the generation and the evolution of continuous-variable (CV) entanglement from a laser-driven four-state atom inside a doubly resonant cavity under Raman excitation. Two transitions in the four-state atom independently interact with the two cavity modes, while two other transitions are driven by coupling laser fields. By including the atomic relaxation as well as cavity losses, we show that the CV entanglement with large mean number of
photons can be generated in our scheme. We also show that the intensity of the coupling laser fields can influence effectively the entanglement period of the cavity field. Different from the conventional resonant excitation scheme where zero one-photon detuning are required, it is found that the intensity and period of entanglement between the two cavity modes as well as the total mean photon number of the cavity field can be adjusted by properly
modulating the frequency detuning.     

Some statistical properties for a spin-(1/2) particle coupled to two spirals

In this paper we consider the problem of the interaction between two SU(2) quantum systems namely: two-level atom and multi-level atoms. The evolution operator is obtained and used to calculate the time-dependent dynamical operators. It has shown that the atomic inversion is sensitive to the change in the detuning parameter ?, the quantum numbers j_k as well as the atomic angles. The atomic squeezing is also considered and the phenomenon of squeezing is observed in both quadrature variances, however, with a periodic exchange between the quadratures. The degree of entanglement is examined by employing von Neumann entropy. It has shown that an increase in the value of the detuning parameter leads to a decrease in the degree of entanglement. However, for a weak coupling parameter the system shows reduction in the entropy. In the meantime the maximum entanglement can be reached when we increase the value for the quantum numbers j_k. Also it has shown that the atomic angles play a role for controlling the degree of entanglement.     

Nonclassical Properties for Two Coupled N-Two-Level Atom and a Single Two-Level Atom Under an External Magnetic Field

We study the interaction between a single two-level atom and N two-level atoms under the effect of a uniform magnetic field. The exact solution is obtained and the expectation value of the time-dependent quantum operators calculated using the Block state (the generalized coherent state). We discuss numerically the atomic inversion where the phenomenon of collapse and revival is observed. The change in the value of the atomic angle plays a role in variance squeezing, where it is pronounced for ?? = π/3. Entropy squeezing is discussed and occurred in the first quadrature. The degree of entanglement through linear entropy is examined where the system shows partial entanglement and at a certain value of parameters displays nearly maximum entanglement.     

Squeezing via coupling of Bose--Einstein condensates in a double-well potential with a cavity light field

Squeezing via the interaction between the cavity light field and the Bose Einstein Condensate （BEC） in a doublewell potential is considered within the context of the two-mode approximation. For the cavity light field initially in a coherent state, it is shown that by choosing appropriate parameters, quadrature squeezing of the cavity light field can be achieved and it exhibits periodic oscillation. We also study the case in which BEC is tuned to resonance by periodically modulating the trapping potentiaL and the quadrature squeezing of the cavity field exhibits periodic collapse and revival effect. Both analytic and numerical calculations are performed, and they are found to be in good agreement with each other. The result shows that the quantum statistical properties of the cavity light field can be manipulated by its coupling with the condensates in the double-well potential. On the other hand, dynamical properties of the condensates in the double-well potential will be reflected by the quadrature squeezing of the light field.