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# Adiabatic Creation of Atomic Squeezing in Dark States vs. Decoherences 

$^{1}$Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China 

Z. R. Gong), 1 Xiaoguang Wang, 2 and C. P. Sun 1 

$^{2}$Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China 

We study the multipartite correlations of the multi-atom dark states, which are characterized by the atomic squeezing beyond the pairwise entanglement. It is shown that, in the photon storage process with atomic ensemble via electromagnetically induced transparency (EIT) mechanism, the atomic squeezing and the pairwise entanglement can be created by adiabatically manipulating the Rabi frequency of the classical light field on the atomic ensemble. We also consider the sudden death for the atomic squeezing and the pairwise entanglement under various decoherence channels. An optimal time for generating the greatest atomic squeezing and pairwise entanglement is obtained by studying in details the competition between the adiabatic creation of quantum correlation in the atomic ensemble and the decoherence that we describe with three typical decoherence channels. 

Atomic ensemble can serve as a quantum memory for storing the quantum information of photons [1–4] where the memory elements can be described as the quasi-spin wave excitations in atomic ensemble [5], or Dicke type collective states [6]. Recent experiments have demon- strated that such storable and quantum memory could have long lifetime for the use in long-distance quantum communication [7]. When using the magnetically insen- sitive clock transition in atomic rubidium confined in a one-dimensional optical lattice, quantum memory life- time can exceed 3 ms [8]. 

The relevant quantum storage process could be im- plemented through the many-particle enhancement of the absorption cross section with the adiabatic-passage techniques [9]. Through the electromagnetically induced transparency (EIT) mechanism, the adiabatic manipula- tion utilizes the dark polariton | d$_{n}$ ( θ ) 〉 (a photon-dressed collective atomic state). With adiabatically changing parameter θ ∈ [0 , π/ 2] , the quantum state of photon | P 〉 = ∑ $_{n}$c$_{n}$ | n 〉 (a superposition of photon Fock states n ) can be adiabatically converted to a state of the col- lective atom excitation | M 〉 = ∑ $_{n}$c$_{n}$ | M$_{n}$ 〉 , which is a superposition of the collective atomic states | M$_{n}$ 〉 with the same coefficients c$_{n}$ as that in the photon state | P 〉 . Mathematically, this coherent conversion of the photon state is an associated mapping 

<img src='content_image/419996.jpg'>

where | d $^{′}$〉 and | p $^{′}$〉 are the initial state of the memory and the final state of photon respectively. Obviously, here only used are the macroscopically coherent proper- ties of each collective excitation, which is described by individual collective state | M$_{n}$ 〉 , rather than the inter- nal entanglement and quantum correlation in the single collective state | M$_{n}$ 〉 as well as | d$_{n}$ ( θ ) 〉 . In this paper we will pay attention to the latter by 

considering the multipartite correlation measured by spin 

PACS numbers: 03.67.Mn, 03.65.Ud, 03.65.Yz 

## I. INTRODUCTION 

squeezing in | M$_{n}$ 〉 , which is obtained from | d$_{n}$ ( θ ) 〉 by adi- abatic manipulation for the dark state | d$_{n}$ ( θ ) 〉 as 

<img src='content_image/419995.jpg'>

We study in details the dynamic competition between the adiabatic creation of quantum correlation in the atomic ensemble and the decoherence that we describe with three typical decoherence channels. There are two time scales t$_{1}$ and t$_{2}$ depicting such competition, where t$_{1}$ repre- sents the adiabatic time limited by the adiabatic condi- tions and t$_{2}$ represents the decoherence time. Actually, if we regard the atomic ensemble as a macroscopic object in large N limit, quantum decoherence scenario seems to result in the quantum disappearance due to noisy ambient environments [10] or the internal random mo- tions [11, 12]. A surprising discovery about the pairwise entanglement is that it suddenly die due to influence of environment [13, 14]. In this paper, we also consider this sudden death phenomena of the pairwise entanglement as well as the atomic squeezing for quantum correlation for more than two particles. We compare the time scales of various sudden death processes with the speed of adi- abatic manipulations for creating such squeezing as well as the pairwise entanglement. 

Actually, creating spin squeezing in a single Dicke like state is the crucial step for the precision measurements based on many-atom spectroscopy. With such controlled production of complex entangled states of matter and light, squeezing the fluctuations via entanglement be- tween 2-level atoms can improve the precision of sens- ing, clocks, metrology, and spectroscopy [15]. This paper seems to provide a simple scheme for adiabatic creation of atomic squeezing. This adiabatic passage manipula- tion seems feasible in creating the spin squeezing, but it requires an ideal technique of single photon source, which can initially produce the single Fock states | n 〉 . Therefore, our present theoretical proposal may meet the difficulty for physical implementation based on the existing tech- nology. 

This paper is arranged as follows. In Sec. II, we study 

