Research progress of Rydberg many-body interaction

Zhang Zheng-Yuan; Zhang Tian-Yi; Liu Zong-Kai; Ding Dong-Sheng; Shi Bao-Sen

doi:10.7498/aps.69.20200649

Abstract

The interaction of many-body quantum system is a critical problem to be solved in the field of quantum information science. Rydberg atoms have large dipole moment, enabling them to interact with others in a long range, thereby offering us a powerful tool for studying many-body quantum physics. Meanwhile, atoms in the ground state are stable, which makes it easy to manipulate them. Therefore, Rydberg-atom many-body system is an ideal platform for studying the interaction of many-body quantum system. Studies of Rydberg-atom many-body system may contribute to understanding the properties of many-body system and putting the interaction of many-body quantum system into practical applications. In this review, we introduce some studies of properties of interaction of Rydberg-atom many-body system, including the Rydberg excitation blockade, the variation of Rabi frequencies of the many-body system and special spatial distribution of Rydberg atoms in a many-body system. Firstly, the Rydberg excitation blockade, the most important property in the Rydberg-atom many-body system, indicates that atoms’ excitation will be suppressed in a certain range around one Rydberg excitation because the interaction between the Rydberg excitation and atoms leads the energy level to shift so that atoms cannot be excited by the same pulse. Secondly, there is a collective Rabi frequency in the system, which is proportional to the square of the number of atoms in the suppressed area. And additionally, because of the Rydberg blockade effect, Rydberg excitations in the ensemble cannot be at casual positions but a regular distribution is formed. Besides the studies of properties, several researches on the applications of interaction of Rydberg-atom many-body system are introduced, including single-photon source, quantum storage, single-atom imaging, quantum simulation, etc. These applications contribute to the development of quantum community and quantum computing, which may bring us a quantum-technology time. Finally, we discuss the future development of Rydberg-atom many-body system and its further applications. Further development includes the development of many-body system with a larger number of atoms, the development of many-body system of atoms with more than one electron, and some other specific subjects based on many-system, such as Rydberg dimer and topological phase. Also some promising applications such as in studying optimization problem by quantum annealing, may become true.

Keywords:

Authors and contacts

CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China

Corresponding author: Ding Dong-Sheng, dds@ustc.edu.cn

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References

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Cited By

图 1 激光激发两原子体系能级示意图

Figure 1. Energy level of two-atoms system excited by one laser.

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图 2 存在频率失谐时的双原子系统能量示意图　(a) 当$\varDelta > 0$且${\rm d}U/{\rm d}R > 0$时双原子系统的能量; (b) 不同频率失谐和势能情况下双原子系统的能量^[19]

Figure 2. Schematic of binary Rydberg energy with detuning: (a) The energy of a pair of atoms with $\varDelta > 0$ and ${\rm d}U/{\rm d}R > 0$; (b) the energy of a pair of atoms with different detuning and potentials^[19].

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图 3 多体态的空间有序分布图^[3]　(a) 直接成像结果; (b) 多次叠加结果; (c) 预测结果

Figure 3. Spatially ordered components of the many-body states^[3]: (a) Directly imaging result; (b) accumulative result of many measurements; (c) predicted result.

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图 4 (a)一维Ising模型配分函数的张量网络表示; (b) 二维Ising模型配分函数的张量元; (c) 二维Ising模型配分函数的张量网络表示^[26]

Figure 4. (a) Tensor network form of the partition function for 1D Ising model; (b) tensor element for the partition function of 2D Ising model; (c) tensor network form of the partition function for 2D Ising model^[26]

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图 5 二维Ising模型的比热随温度倒数的变化^[27]

Figure 5. Relationship between the specific heat and the reciprocal of the temperature^[27].

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图 6 单光子源性质参数　(a) ${g^{\left( 2 \right)}}\left( 0 \right)$与有效主量子数n^*关系^[30], 内插图为重合光子计数与延时关系^[30]; (b) 量子点方案中归一化的重合光子计数与延时关系^[28]; (c) 量子点方案中平行和交叉极化情况下Hong-Ou-Mandel干涉归一化的重合光子计数与延时关系^[28]

Figure 6. Parameters of single-photon source: (a) ${g^{\left( 2 \right)}}\left( 0 \right)$ as a function of effective principle quantum number^[30]. Coincidence count as a function of time decay is showed in the inset^[30]; (b) normalized coincidence count as a function of time decay using quantum dots^[28]; (c) normalized coincidence count of Hong-Ou-Mandel interference as a function of time decay with parallel and cross polarization respectively using quantum dots^[28].

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图 7 量子存储性质随入射光子数N_in变化^[47]　(a) 存储效率与存储时间关系; (b) 存储效率与Rydberg态关系

Figure 7. Properties of quantum storage with different number of input photons N_in^[47]: (a) Storage efficiency as a function of storage time; (b) storage efficiency as a function of Rydberg states.

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图 8 基态与激发态结合能级示意图^[4]　(a) 写入过程; (b) 基态存储; (c) 读出过程

Figure 8. Schematic of energy levels combined exciting state with ground state^[4]: (a) Procedure of writing; (b) storage in the ground state; (c) procedure of read.

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图 9 成像示意图与模拟结果^[6]　(a) 单原子成像过程示意图; (b) 没有控制光情况下的探测光吸收图; (c) 有控制光情况下的探测光吸收图

Figure 9. Scheme of imaging process and simulated results^[6]: (a) Scheme of single-atom imaging process; (b) absorption of probe light without control light; (c) absorption of probe light with control light.

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图 10 (a) 不同源光子数情况下, 恢复门光子数与存储门光子数关系^[7]; (b) 最佳减法效率对比^[7]

Figure 10. (a) Number of retrial gate photons ${\bar a_{\rm g}}$ as a function of number of stored gate photons ${a_{\rm s}}$ with different number of source photons ${a_{\rm s}}$^[7]; (b) contrast of optimal efficiency of subtraction^[7].

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图 11 相图^[10]和自组织行为^[64]　(a) Rydberg原子密度相图; (b) 没有控制光时EIT相图; (c) 自组织演化; (d) 自组织定态规律

Figure 11. phase diagram^[10] and self-organized behaviors^[64]: (a) Phase diagram of density of Rydberg atom; (b) EIT phase diagram without control light; (c) evolution in the self-organized process; (d) regulation of self-organized stationary states.

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图 12 二维量子模拟^[63]　(a) 不同原子数的集体拉比振荡; (b) 20个原子系统的Rydberg分数${f_{\rm R}}$变化; (c) 28个原子系统的Rydberg分数${f_{\rm R}}$变化

Figure 12. Quantum simulation in two dimensions^[63]: (a) Collective Rabi oscillation with different number of atoms; (c) Rydberg fraction of the systems with 20 atoms; (d) Rydberg fraction of the systems with 28 atoms.

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图 13 一维多原子量子模拟^[9]　(a) 不同相互作用强度的演化理论结果; (b) 不同相互作用强度的演化实验结果; (c) 基态概率与系统大小的关系; (d) 出现次数的状态数的统计

Figure 13. Many-atom quantum simulation in one dimension^[9]: (a) Predicted results of evolution with different interaction; (b) experimental results of evolution with different interaction; (c) ground-state probability as a function of system size; (d) number of states with identical number of occurrences.

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表 1 Rydberg原子的性质和主量子数的关系^[11].

Table 1. Relation between the properties of Rydberg atom and its principal quantum number^[11].

性质	与主量子数关系	Na(10 d)
束缚能	n^–2	0.14 eV
相邻n态间的能量差	n^–3	0.023 eV
轨道半径	n²	147a₀
几何截面	n⁴	68000$a_0^2$
偶极矩$\left\langle {nd\left\| {er} \right\|\left. {nf} \right\rangle } \right.$	n²	143ea₀
极化率	n⁷	0.21 MHz·cm²·V^–2
辐射寿命	n³	1.0 μs
精细结构间隔	n^–3	–92 MHz

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[4]	Li L, Kuzmich A 2016 Nat. Commun. 7 13618 Google Scholar
[5]	Maxwell D, Szwer D J, Paredes-Barato D, Busche H, Pritchard J D, Gauguet A, Weatherill K J, Jones M P A, Adams C S 2013 Phys. Rev. Lett. 110 103001 Google Scholar
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[8]	Keesling A, Omran A, Levine H, Bernien H, Pichler H, Choi S, Samajdar R, Schwartz S, Silvi P, Sachdev S, Zoller P, Endres M, Greiner M, Vuletić V, Lukin M D 2019 Nature 568 207 Google Scholar
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[12]	Christoph T 2017 Ph. D. Dissertation (Stuttgart: University of Stuttgart. Physical Institute)
[13]	Gallagher T F 1988 Rep. Prog. Phys. 51 143
[14]	Gallagher T F, Cooke W E 1979 Phys. Rev. Lett. 42 835 Google Scholar
[15]	Cooke W E, Gallagher T F 1980 Phys. Rev. A 21 588
[16]	Born M, Oppenheimer J R 1927 Ann. Phys. 84 457
[17]	Thomas A 2008 Ph. D. Dissertation (Freiburg city: Faculty of Mathematics and Physics Albert Ludwigs University of Freiburg)
[18]	Browaeys A, Lahaye T 2020 Nat. Phys. 16 132 Google Scholar
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