^{1}, Huaibin Zheng

^{1,a)}, Zhaoyang Zhang

^{1}, Xin Yao

^{1}, Yunzhe Zhang

^{1}, Yiqi Zhang

^{1}and Yanpeng Zhang

^{1,a)}

### Abstract

We investigate the interaction between dark states and Rydberg excitation blockade by using electromagnetically induced transparency (EIT), fluorescence, and four-wave mixing (FWM) signals both theoretically and experimentally. By scanning the frequency detunings of the probe and dressing fields, respectively, we first observe these signals (three coexisting EIT windows, two fluorescence signals, and two FWM signals) under Rydberg excitation blockade. Next, frequency detuning dependences of these signals are obtained, in which the modulated results are well explained by introducing the dressing effects (leading to the dark states) with the corrected factor of the Rydberg excitation blockade. In addition, the variations by changing the principal quantum number n of Rydberg state shown some interesting phenomena resulting from Rydberg blockade are observed. The unique nature of such blockaded signals can have potential application in the demonstration of quantum computing.

This work was supported by the 973 Program (2012CB921804), and the National Science Foundation of China (NSFC) (11104216, 61078002, 61078020, 11104214, 61108017, and 61205112).

I. INTRODUCTION

II. BASIC THEORY AND EXPERIMENTAL SCHEME

III. RESULTS AND DISCUSSIONS

IV. CONCLUSION

### Key Topics

- Rydberg states
- 56.0
- Fluorescence
- 34.0
- Four wave mixing
- 23.0
- Dark states
- 5.0
- Laser beam effects
- 5.0

##### G02F1/35

## Figures

(a) Spatial beam geometry used in the experiment. (b) The diagram of the X-type five-level system.

(a) Spatial beam geometry used in the experiment. (b) The diagram of the X-type five-level system.

(a) From top to bottom in each column, there are measured signals of probe, FWM E F4, FWM E F3, and fluorescence versus Δ1, respectively, in which the differences among (a1)–(a5) are that the variable of (a1)–(a3) is the detuning Δ4 with level |2⟩ being 37D, and (a4)–(a5) is the principal quantum number n (45D and 54D, respectively) corresponding to (a1). (b11)–(b41) Fluorescence signal R1 modulated by E 2 versus Δ1 and (b12)–(b42) pure Rydberg EIT versus Δ1 at four discrete principal quantum numbers n. (c) Dependences of (b11)–(b41) fluorescence and (b12)–(b42) EIT on the principal quantum number n.

(a) From top to bottom in each column, there are measured signals of probe, FWM E F4, FWM E F3, and fluorescence versus Δ1, respectively, in which the differences among (a1)–(a5) are that the variable of (a1)–(a3) is the detuning Δ4 with level |2⟩ being 37D, and (a4)–(a5) is the principal quantum number n (45D and 54D, respectively) corresponding to (a1). (b11)–(b41) Fluorescence signal R1 modulated by E 2 versus Δ1 and (b12)–(b42) pure Rydberg EIT versus Δ1 at four discrete principal quantum numbers n. (c) Dependences of (b11)–(b41) fluorescence and (b12)–(b42) EIT on the principal quantum number n.

(a) K2 EIT signals versus Δ2 are obtained at different values of the detuning Δ1 in each panel. (a1)–(a4) correspond to n = 37D, 45D, 54D, and 63D, respectively. (b) Theoretical calculations corresponding to the experimental data shown in (a). (c) Principal quantum number dependences of k2 EIT signals obtained at seven discrete detuning values of Δ1, in which the upper curves are the orignal data and the lower ones are the values scaled with the dipole transition probability. (d) Theoretical calculations corresponding to the results shown in (c). (e)–(h) The fluorescence signals R1 obtained with the same method as k2 EIT.

(a) K2 EIT signals versus Δ2 are obtained at different values of the detuning Δ1 in each panel. (a1)–(a4) correspond to n = 37D, 45D, 54D, and 63D, respectively. (b) Theoretical calculations corresponding to the experimental data shown in (a). (c) Principal quantum number dependences of k2 EIT signals obtained at seven discrete detuning values of Δ1, in which the upper curves are the orignal data and the lower ones are the values scaled with the dipole transition probability. (d) Theoretical calculations corresponding to the results shown in (c). (e)–(h) The fluorescence signals R1 obtained with the same method as k2 EIT.

The experimentally measured probe transmission (a) and fluorescence signals (e) by scanning Δ2 under different discrete points Δ4 in Y-type four energy level system. (b) and (f) are the theoretically calculated results of (a) and (e). From ((a1), (b1), (e1), (f1)) to ((a4), (b4), (e4), (f4)), the principal quantum numbers are n = 37, 45, 54, and 63, respectively. The dependence curves of the EIT peak height (c) and (d) and fluorescence strength (g) and (h) on principal quantum number n corresponding to (a) and (b) and (e) and (f), respectively, in which the seven panels are corresponding to the signals at the left, right sides of large detuning, or the left, left-top, right, right-top, and top of the EIT signals.

The experimentally measured probe transmission (a) and fluorescence signals (e) by scanning Δ2 under different discrete points Δ4 in Y-type four energy level system. (b) and (f) are the theoretically calculated results of (a) and (e). From ((a1), (b1), (e1), (f1)) to ((a4), (b4), (e4), (f4)), the principal quantum numbers are n = 37, 45, 54, and 63, respectively. The dependence curves of the EIT peak height (c) and (d) and fluorescence strength (g) and (h) on principal quantum number n corresponding to (a) and (b) and (e) and (f), respectively, in which the seven panels are corresponding to the signals at the left, right sides of large detuning, or the left, left-top, right, right-top, and top of the EIT signals.

The measured probe transmission (a), fluorescence (b), and FWM E F4 (c) signals with Δ4 scanned at different Δ1. (d), (e), and (f) are the theoretically calculated results corresponding to (a), (b), and (c). From ((a1), (b1), (c1), (d1), (e1), and (f1)) to ((a4), (b4), (c4), (d4), (e4), and (f4)), the principal quantum numbers are n = 37, 45, 54, and 63, respectively.

The measured probe transmission (a), fluorescence (b), and FWM E F4 (c) signals with Δ4 scanned at different Δ1. (d), (e), and (f) are the theoretically calculated results corresponding to (a), (b), and (c). From ((a1), (b1), (c1), (d1), (e1), and (f1)) to ((a4), (b4), (c4), (d4), (e4), and (f4)), the principal quantum numbers are n = 37, 45, 54, and 63, respectively.

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