Atomic squeezed states in a driven Dicke model

We consider the dissipative N two-level atom Dicke system driven by a c.w. laser field. In the steady state, the cooperativity among the atoms via the radiation field produces spin squeezing. Even in the absence of dipole-dipole interaction, the system shows spin squeezing which is attributed to strong nonlinear interaction with the driving field.     

Single-atom entropy squeezing for two two-level atoms interacting with a single-mode radiation field

In this paper we consider a system of two two-level atoms interacting with a single-mode quantized electromagnetic field in a lossless resonant cavity via l-photon-transition mechanism. The field and the atoms are initially prepared in the coherent state and the excited atomic states, respectively. For this system we investigate the entropy squeezing, the atomic variances, the von Neumann entropy and the atomic inversions for the single-atom case. Also we comment on the relationship between spin squeezing and linear entropy. We show that the amounts of the nonclassical effects exhibited in the entropy squeezing for the present system are less than those produced by the standard Jaynes-Cummings model. The entropy squeezing can give information on the corresponding von Neumann entropy. Also the nonclassical effects obtained from the asymmetric atoms are greater than those obtained from the symmetric ones. Finally, the entropy squeezing gives better information than the atomic variances only for the asymmetric atoms.     

Nonclassical effects in a highly nonlinear generalized homogeneous Dicke model

An intensity dependent nonlinear coupling model of N two-level atoms (generalized Dicke model) interacting dispersively with a bimodal cavity field via two-photon transitions is investigated in a scenario where the rotating wave approximation is assumed. The model becomes homogeneous in the sense that the spin transition frequency is the same for all atoms and the coupling constants emerging from the collective interactions of the atomic system with the cavity field depend only on the particular radiation field mode. This allows us to represent the Dicke Hamiltonian entirely in terms of the total angular momentum J. It is assumed that, initially, the atomic system and the field are in a disentangled state where the field modes are in Glauber coherent states and the atomic system is a superposition of states |JM〉 (Dicke states). The model is numerically tested against simulations of normal squeezing variance of the field, squeezing factors based on the Heisenberg uncertainty principle, along with the statistical properties of the light leading to the possible production of nonclassical effects, such as degree of second-order coherence in the modes, degree of intermode correlation, as well as violation of the Cauchy–Schwartz inequality. Analytical expression of the total density operator matrix elements at t>0 shows the present nonlinear model to be strongly entangled, which is reflected in the time evolution of the linear entropy, where the superposition states are reduced to statistical mixtures. Thus, the present generalized Dicke model does not preserve the modulus of the Bloch vector. The computations, performed in the weak coupling and strong field limits, were conducted via second-order Dyson perturbative expansion of the time evolution operator matrix elements for the totality of the angular momentum states of the atomic system.     

Atomic coherent states and reduced quantum fluctuations in optical transients

We show that the atomic coherent states (the Bloch states) commonly encountered in coherent transient phenomena exhibit squeezing. We illustrate this property calculating the degree of squeezing and the normalized correlation coefficient g⁽²⁾ for a system of N two-level atoms interacting with a cw laser electric field.     

Generation of squeezed atomic states in cavity QED

A squeezed atomic state is that state of a system of two-level atoms for which the intrinsic quantum noise in a process of measurement is less than the minimum noise obtained by using a spin coherent state. It is shown that such a state is generated in certain time intervals when a non-squeezed atomic state evolves on interaction with a single mode coherent field inside a lossless cavity. The atoms are assumed to undergo one-photon or two-photon transitions between the given two levels. The maximum atomic squeezing is found as a function of the number of atoms and the field strength. The effect of the field-dependent Stark shift is investigated in the case of the atoms undergoing two-photon transitions.     

Atomic squeezing in assembly of two two-level atoms interacting with a single mode coherent radiation

Saito and Ueda [Phys. Rev. A 59, 3959 (1999)] studied atomic and radiation squeezing in interaction of a single mode coherent state of radiation with two excited two-level atoms, using the Jaynes Cummings Hamiltonian. They considered α real and studied squeezing of the Dicke operator S_x using the Kitagawa-Ueda criterion for squeezing and coupling times less than or nearly equal to . We obtain results to all orders in coupling time for atoms, which are initially in (i) fully excited, (ii) superradiant or in (iii) ground states and obtain more general results. We use our recently reported criterion for atomic squeezing, of which the Kitagawa-Ueda criterion is a special case, and obtain a much stronger (nearly 95%) atomic squeezing than that (nearly 1.1%) reported by Saito and Ueda.     

Variance squeezing and information entropy squeezing via Bloch coherent states in two-level nonlinear spin models

The nonclassical squeezing effect emerging from a nonlinear coupling model (generalized Jaynes–Cummings model) of a two-level atom interacting resonantly with a bimodal cavity field via two-photon transitions is investigated in the rotating wave approximation. Various Bloch coherent initial states (rotated states) for the atomic system are assumed, i.e., (i) ground state, (ii) excited state, and (iii) linear superposition of both states. Initially, the atomic system and the field are in a disentangled state, where the field modes are in Glauber coherent states via Poisson distribution. The model is numerically tested against simulations of time evolution of the based Heisenberg uncertainty relation variance and Shannon information entropy squeezing factors. The quantum state purity is computed for the three possible initial states and used as a criterion to get information about the entanglement of the components of the system. Analytical expression of the total density operator matrix elements at t > 0 shows, in fact, the present nonlinear model to be strongly entangled, where each of the definite initial Bloch coherent states is reduced to statistical mixtures. Thus, the present model does not preserve the modulus of the Bloch vector.     

Pairwise entanglement in symmetric multi-qubit systems

For pairs of particles extracted from a symmetric state of N two-level systems, the two-particle density matrix is expressed in terms of expectation values of collective spin operators for the large system. Results are presented for experimentally relevant examples of pure states: Dicke states | S, M>, spin coherent, and spin squeezed states, where only the symmetric subspace, S = N/2 is populated, and for thermally entangled mixed states populating also lower S values. The entanglement of the extracted pair is then quantified by a calculation of the concurrence, which provides directly the entanglement of formation of the pair. Received 9 May 2001 and Received in final form 16 November 2001     

Quantum phase properties of the field in a two-photon micromaser

In this paper, we study the quantum phase properties of the field in a two-photon micromaser, including the effects of the finite detuning of the intermediate level. For initial coherent state of the cavity field and atoms initially in their excited state multipeak phase structure appears which eventually leads to the randomization of the cavity field phase. However, the approach towards the randomization depends upon the detuning. If the atoms are injected in a coherent superposition of their upper and lower atomic states then the phase distribution evolves into two-peak structure. For initial thermal state and atoms in polarized state, cavity field acquires some phase. We also consider the effect of finite Q of the cavity, random injection of the atoms and fluctuations in the interaction time.     

Kerr介质中双模纠缠相干光与Bell态原子相互作用系统的原子偶极压缩

运用全量子理论并结合数值计算方法，研究了Kerr介质腔中处于Bell态的两个全同二能级纠缠原子与双模纠缠相干光场相互作用系统的原子偶极压缩特性.讨论了双原子体系的初态、光场的平均光子数、双模纠缠相干光场的纠缠程度以及Kerr介质与双模光场的耦合强度对原子偶极压缩特性的影响.结果表明：双原子体系的初态为|β₁₁>时，不会出现偶极压缩效应；初态为|β₀₀>，|β₀₁>或|β₁₀>时在一定条件下可能出现原子压缩效应，且此时原子压缩的特性与Kerr介质与双模光场的耦合强度、初始光场的平均光子数、双模纠缠相干光场的纠缠程度有关. 关键词： 量子光学 Bell态 双模纠缠相干光场 Kerr介质     

Probabilistic teleportation of an arbitrary superposition of symmetric two-atom Dicke states in cavity QED

A scheme is discussed for probabilistic teleportation of a special type of two-atom pure state - an arbitrary superposition of symmetric two-atom Dicke states. The scheme follows the previous idea [S.B. Zheng, Phys. Rev. A 69 (2004) 064302], which is proposed for approximate and probabilistic teleportation of an atomic state through only a detection on the sender atom. In principle, the present scheme can achieve faithful teleportation by resorting to a very different model, which depicts the resonant interaction of a Λ-type three-level atom with a two-mode cavity field. The scheme can also be used for teleportation of an arbitrary superposition of symmetric multi-atom Dicke states.     

Conditional spin squeezing of a large ensemble via the vacuum Rabi splitting

We use the vacuum Rabi splitting to perform quantum nondemolition measurements that prepare a conditionally spin squeezed state of a collective atomic psuedospin. We infer a 3.4(6) dB improvement in quantum phase estimation relative to the standard quantum limit for a coherent spin state composed of uncorrelated atoms. The measured collective spin is composed of the two-level clock states of nearly 10(6) (87)Rb atoms confined inside a low finesse F=710 optical cavity. This technique may improve atomic sensor precision and/or bandwidth, and may lead to more precise tests of fundamental physics.     

Correspondence between generalized binomial field states and coherent atomic states

We show that the N-photon generalized binomial states of electromagnetic field may be put in a bijective mapping with the coherent atomic states of N two-level atoms. We exploit this correspondence to simply obtain both known and new properties of the N-photon generalized binomial states. In particular, an over-complete basis of these binomial states and an orthonormal basis are obtained. Finally, the squeezing properties of generalized binomial state are analyzed.     

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.     

A source of nonclassical radiations exhibiting photon antibunching

We show that coherent spontaneous emission by a two-level atomic system in a Dicke state placed in a resonant cavity gives a non-classical radiation exhibiting photon-antibunching. It is assumed that the “effective” population of the ground state atoms is initially large compared to unity.     

Effects of Purity on Dynamics of Multipartite Entanglement

We study the effects of purity on entanglement dynamics of a multipartite system in cavity QED. Three two-level atoms A, B and C are initially prepared in an entangled state and locally coupled with independent cavities a, b and c, respectively. We consider the effects of purity of atomic initial state on the entanglement evolution of both the systems of atoms and cavities. It is found that depending on the purity of atomic initial state, the entanglement of atoms （cavities） may or may not exhibit the sudden death （birth） phenomenon.     

依赖强度耦合三光子过程下运动原子最佳熵压缩态的制备

为了研究三光子过程中原子与相干态耦合量子体系信息熵压缩随时间演化规律及原子最佳信息熵压缩态的制备,我们采用全量子理论,推导出运动原子与单模简并三光子依赖强度耦合量子体系的精确解;理论上给出制备原子最佳信息熵压缩态的充分及必要条件,并进行了数值模拟验证.研究结果表明:控制相干态场与原子作用时间,切断相干态场与原子的纠缠,选择二能级原子处于等权重相干叠加态,适当选取相干态场与原子的初始位相,可以制备出原子最佳量子信息熵压缩态;调节光腔中场模结构参量,能够得到连续的量子信息熵压缩态.该研究结果在多光子过程低噪声量子信息处理中具有一定意义.     

The effect of the counter-rotating terms on the Rabi oscillations and squeezing in the Dicke model with cavity losses

The effect of the counter-rotating terms in the Dicke model with cavity losses is examined. Numerical results for the time evolutions of the atomic population inversion, dipole moment, mean-photon number and atomic and field squeezing parameters for an initial coherent field are presented for various numbers of atoms and different cavity dampings. As a consequence of the counter-rotating terms, the appearance of new steady states for atomic population inversion and the mean-photon number is pointed out.     

Exact results on decoherence and entanglement in a system of N driven atoms and a dissipative cavity mode

We solve the dynamics of an open quantum system where N strongly driven two-level atoms are equally coupled on resonance to a dissipative cavity mode. Analytical results are derived on decoherence, entanglement, purity, atomic correlations and cavity field mean photon number. We predict decoherencefree subspaces for the whole system and the N-qubit subsystem, the monitoring of quantum coherence and purity decay by atomic populations measurements, the conditional generation of atomic multi-partite entangled states and of cavity cat-like states. We show that the dynamics of atoms prepared in states invariant under permutation of any two components remains restricted within the subspace spanned by the completely symmetric Dicke states. We discuss examples and applications in the cases N = 3, 4. An erratum to this article can be found at     

原子与弱相干腔场相互作用系统中的量子特性

考虑腔场处于弱相干态的情况,研究了两个全同的二能级原子与耦合腔相互作用系统中原子的偶极压缩和原子间的纠缠特性。研究结果表明,随耦合腔耦合系数增大,原子的偶极压缩减弱。另一方面,随耦合腔耦合系数增大,原子间的纠缠也减弱,这一结果与耦合腔处于真空态的情况相反。