Detecting the quantumness of an atomic ensemble
Chang-Hau Kuo1,2*, Yao-Chun Yu1,2, Guang-Yin Chen2,3, Yueh-Nan Chen2,4, Che-Ming Li2,5, Jung-Jung Su6, Chih-Sung Chuu1,2
1Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
2Center for Quantum Technology, National Tsing Hua University, Hsinchu, Taiwan
3Department of Physics, National Chung Hsing University, Taichung, Taiwan
4Department of Physics, National Cheng-Kung University, Tainan, Taiwan
5Department of Engineering Science, National Cheng-Kung University, Tainan, Taiwan
6Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan
* Presenter:Chang-Hau Kuo, email:ch.kuo@mx.nthu.edu.tw
Abstract: Atomic ensemble interacting with nonclassical light provides an interesting platform for exploring the quantumness of macroscopic systems. We propose several methods to identify the quantum nature of an atomic ensemble induced by the absorption of a single photon. We show that the extended Leggett-Garg inequality and quantum coherence witness both provide useful means to characterize the quantum nature. Our calculation also shows that, while higher optical density provides stronger indication of quantumness, lower optical density can prolong the presence of quantumness.
Keywords: Superradiance, Single photon, Leggett-Garg Inequality, Quantum Coherence Witness.
1. Introduction
Quantum mechanics has been successful in describing microscopic world such as an atom or an electron. However, when it is applied to macroscopic systems, one usually arrives at contradictions to everyday common sense. A well-known example is the Schrodinger's cat, in which a macroscopic object like a cat can be simultaneously alive and dead or in a superposition of “alive state” and “dead state”. Such quantum weirdness was first studied by Leggett and Garg in their seminal paper [1], in which they considered successive measurements on a single macroscopic system at various times.
Atomic ensemble interacting with nonclassical light provides another promising platform for demonstrating the quantumness of macroscopic systems. When the atoms are uniformly excited by a single photon at different times, a highly entangled state is formed. This timed Dicke state does not possess a dipole moment, as opposed to the superadiance state considered by Dicke [2]. Nevertheless, such system exhibits many interesting properties, including the directed spontaneous emission, dynamical oscillation, photon localization, collective Lamb shift and associated radiative decay, and single-photon subradiance, and has also been the subjects of quantum memory and entangled-photon generation.
Here, we exploit the extended LGI [3, 4] and quantum coherence witness [5] to study the single-photon-induced quantum coherence in a macroscopic atomic ensemble. These approaches avoid the need of noninvasive measurements and are thus advantageous for reducing the complexity of experimental realization. In addition, we explore the regions of parameters where the quantumness may be disclosed experimentally. Our study shows that, while higher optical density provides stronger indication of quantumness, lower optical density can prolong the presence of quantumness.
2. Technical Work
We consider an atomic ensemble with a cylindrical shape of radius R and length L. The quantum coherence of the atomic ensemble is established by absorbing a single photon (wave vector k ⃗_0 and angular frequency ω_0) incident along the symmetry z -axis. The absorption results in a single collective excitation among the atoms described by the timed Dicke state |+〉=1/√N ∑_(j=1)^N▒〖e^(ik ⃗_0∙r ⃗_j ) |g_1 g_2…e_j…g_N 〉 〗, where N is the atom number, r ⃗_j is the position of the jth atom, and g_j and e_j denote for the ground and excited states, respectively. By the light-matter interaction Hamiltonian, the wave function of the timed Dicke state can be obtained by the time-dependent Schrodinger equation. We also show the properties of the timed Dicke state, for example the splitting spectrum, the Lorentzian distribution of density of state and strongly correlated to its characteristic momentum. With these features, the system can be described in a three-level cavity QED system [6]. Next, we exploit the extended Leggett-Garg Inequality (LGI) [3,4] and quantum coherence witness [5] to test the three-level cavity QED system. The results are in the following Figs. 1. The violation of the extended LGI and the non-zero area of Type-I and II quantum coherence witness are the evidences of existence of the quantum coherence.
Fig. 1 (a,c) the extended LGI. The inequality is violated while the value greater than 1in the dark (red) region. For (b) Type-I and (d) Type-II Quantum coherence witness. All calculations assume cold 87Rb atoms, λ_0=780-nm incident photon, F =R^2/Lλ_0=1 and L = 2 cm. The OD is 130 in (a,b,d)
3. Conclusions
In summary, we have studied the quantum coherence of an atomic ensemble induced by a single photon using the extended LGI and quantum coherence witness. While both approaches are feasible for experimental realization, the sensitivity of quantum coherence witness is higher in terms of the duration of detection. Our calculation also shows that, although higher optical density provides stronger indication of quantumness, lower optical density can prolong the presence of quantumness and may be more favorable for experimental observation.
References
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Keywords: Superradiance, Single photon, Leggett-Garg Inequality, Quantum Coherence Witness