PHYSICAL REVIEW A 91, 033625 (2015)

Detuning-enhanced cavity spin squeezing

Yan-Lei Zhang,1,2 Chang-Ling Zou,1,2,3,* Xu-Bo Zou,1,2,† Liang Jiang,3 and Guang-Can Guo1,2 1Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People’s Republic of China 2Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China 3Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA (Received 28 July 2014; published 23 March 2015)

The unconditional squeezing of the collective spins of an atomic ensemble in a driven [I. D. Leroux, M. H. Schleier-Smith, and V. Vuletic,´ Phys.Rev.Lett104, 073602 (2010)] is studied and analyzed theoretically. Surprisingly, we find that the largely detuned driving laser can improve the scaling of cavity squeezing from S−2/5 to S−2/3,whereS is the total atomic spin. Moreover, we also demonstrate that the experimental imperfection of photon scattering into free space can be efficiently suppressed by detuning.

DOI: 10.1103/PhysRevA.91.033625 PACS number(s): 42.50.Dv, 06.20.−f, 32.80.Qk, 42.50.Lc

I. INTRODUCTION addition, we find that the spin squeezing will be enhanced if the are weakly coupled to the cavity or the laser Large ensembles of atoms are good platforms for quantum detuning is very large. From our numerical solutions and information processing [1–3], due to the long coherence time analytical analysis, the large detuning is very important of atomic energy levels and the collective enhanced interaction because the squeezing originates from the laser induced spin with light. Therefore, the atomic ensemble has been studied state dependent geometry phase [30,31]. Finally, we study extensively for both fundamental physics research [4] and the influence of scattering of a photon into free space due to practical applications, such as quantum memory [1], atomic imperfect Raman scattering, and demonstrate that the optimal clocks [5,6], magnetometers [7,8], and gravitational wave spin squeezing can be obtained with appropriate detuning. detectors [9]. For those metrology applications, it is believed This improvement of spin squeezing by detuning, without the that the classical limitation of measurement precision can requirement of preparation or postselection of the photon state, be broken by using quantum states of the atomic ensem- is very feasible for experiments. The detuning-enhanced cavity ble [10,11]. The squeezed spin state (SSS) [12] is one type of spin squeezing can also be applied to other systems, such such a quantum correlated state with reduced fluctuations in as nitrogen-vacancy centers in diamond, to prepare SSS for one axis of the collective spin components, and it has therefore quantum metrology. attracted considerable attention recently. To prepare the SSS, a variety of experiment schemes based on light-matter interaction have been proposed and II. MODEL demonstrated [10]. One approach is transfer the quantum The system [Fig. 1(b)] is an ensemble of N identical three- state of light to the atomic spins directly [13–16], where level atoms trapped inside an optical Febry-Perot´ cavity. There the degree of spin squeezing is determined by the quality of are two stable ground states |↑ and |↓, which are coupled squeezed input light. Another approach is to generate the SSS to the excited state |e via optical transitions of frequencies by the quantum nondemolition measurement on the states of ω ± ω /2. The cavity frequency ω is chosen so photons coupled with the atomic ensemble [17–22]. While c a c that the detunings to transitions |↑ ↔ |e and |↓ ↔ |e are this method has already been demonstrated by several groups, opposite in sign but having the same