冷原子钟的转轴衰减影响： Ramsey干涉对比度的精确计算

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本文主要探讨了在脉冲光泵浦冷原子钟中，瑞利干涉效应与原子样品的横向衰减之间的相互作用。原子钟中的瑞利干涉是利用原子在电磁场中的精细结构，通过一系列的激光脉冲实现高精度的时间测量技术。然而，当原子在空间分布上并非均匀，而是存在一定程度的横向扩散，即所谓的“transverse decay”，这会显著影响钟的稳定性和精度。作者研究的焦点在于如何量化和理解这种横向衰减对瑞利干涉对比度的影响。他们通过理论计算，详细分析了不同横向衰减速率下的瑞利干涉图案，揭示了这种衰减如何随时间演变以及它对信号强度和频率稳定性的影响。这项工作对于优化冷原子钟设计和提高其长期稳定性的实际应用具有重要意义。实验数据的深入分析是论文的核心部分，通过实际测量的数据拟合，研究人员获得了冷原子样品中横向衰减的速率，大约为每秒30.5次，这个值相较于传统的细胞环境中的衰减要小得多。这一发现暗示着，在冷原子环境下，通过精确控制和减少横向扩散，可以显著提升冷原子钟的性能。此外，该研究还引用了相关的光学科学领域代码（020.0020和270.0270），并指出了文章发表于《中国光学 letters》杂志，接收日期为2012年2月16日，最终接受并在线发布于2012年8月3日。这表明该研究不仅在学术上有价值，也反映了当时中国在量子光学领域的前沿进展。这篇论文为理解冷原子钟在实际操作中的干扰因素提供了深入见解，并为提高这类精密测量设备的性能提供了关键参数。这对于推动原子物理学、精密测量以及量子信息技术的发展具有重要参考价值。

COL 10(10), 100201(2012) CHINESE OPTICS LETTERS October 10, 2012

Ramsey interaction with transverse decay

Xucheng Wang (



RRR

¤¤¤

)

, Huadong Cheng (

¤¤¤

uuu

ÀÀÀ

)

, and Liang Liu (

444 

)

1,2∗

Key Laboratory of Quantum Optics, Shanghai Institute of Optics and Fine Mechanics, and Center of Cold Atom Physics,

Chinese Academy of Sciences, Shanghai 201800, China

State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China

∗

Corresponding author: liang.liu@siom.ac.cn

Received February 16, 2012; accepted March 17, 2012; posted online August 3, 2012

The Ramsey fringe contrast of a pulsed optically pumped cold atom clock is strongly affected by the

transverse decay of the atomic sample. This letter calculates the Ramsey fringe with focus on transverse

decay, and analyzes the Ramsey fringe contrast with different transverse decay rates. By fitting the

experimental data, we obtain the transverse decay rate in a cold atom sample at an approximate value of

30.5 s

−1

, which is much smaller than that in a cell.

OCIS codes: 020.0020, 270.0270.

doi: 10.3788/COL201210.100201.

A typical microwave atomic clock uses the transition be-

tween two ground states as s ignal to lock the local os-

cillator. The spectra l width, signal-to-noise ratio (SNR),

and contr ast are the key factors determining clock p e r-

formance. The width is directly related to the interac-

tion duration between the atoms and the microwave. The

Ramsey method has been widely used in microwave beam

clocks

[1]

and, recently, in cell or cold atom clocks. A typ-

ical cesium beam clo ck has two microwave cavities sepa-

rated by L, and a cesium beam passes through the cav-

ities with speed v

[2]

. The width of the Ramsey fringe is

determined by T = L/v. Similarly, the atomic fountain

[3]

uses a single cavity but passes twice during the upward

and downward motions o f the cold atoms.

The Ramsey fringe contrast is affected by decoher-

ence during the e volution of atoms between two Ramsey

pulses. Theoretically, however, contrast is not consider e d

in the cesium beam clock, because the coherence time is

longer than the evolution time, which is similar in the

atomic fountain clock

[3]

Recently, compact cold atom clocks have re-

ceived considerable attention due to their po tential

applications

[4−7]

. The compact cold atom clock has small

volume, low weight, and high performance prope rties. In

typical atom cooling, the interrogation and detection of

a compact cold atom clock are conducted in same zone.

Thus, decoherence during evolution is an important fac-

tor.

Coherence during evolution is affected by s e veral fac-

tors, such as atom collision, external electromagnetic

field, temperature and density of atomic samples

[8,9]

and others. Generally, decoherence time is described by

transverse decay rate, which can be determined through

an experiment.

In this letter, we introduce a transverse decay rate,

γ, to describe decoherence in the evolution between two

Ramsey pulses. We also study the Ramsey fringe con-

trast r e sulting from γ and compared it with experimental

result. Finally, we estimate γ by fitting the experimental

data with theory.

The up and down levels of a two-level atom system

are represented by |1i and |2i, respectively. The density

matrix is expressed as

ρ =





. (1)

The hyperfine states that |1i and |2i have eigenva lues of

and E

, respectively, and E

− E

= ~ω

, ω

is the

hyp e rfine transition frequency between states |1i and |2i.

The interaction between a two-level atom and a

microwave field is described by the optical Bloch

equations

[10]

given by

d(ρ

− ρ

)

= 2i(V

− V

), (2)

dρ

= −i(ω

+ γ)ρ

+ iV

(ρ

− ρ

), (3)

where the perturbation term V

is expressed as

+ ib

−iωt

, (4)

and ω is the frequency of the microwave field. Here, b

and b

have

= b cos φ, (5)

= −b sin φ, (6)

where b is the Rabi freq uency, and φ is the phase of

the microwave field. In Eq. (3), γ is introduced to

describe atom decoherence, which is sometimes called

transverse decay rate. In a previous work

[10]

, γ is ne-

glected. This method is a lso applied to cesium bea m

or fountain clocks

[11]

, because the cohere nt times for

these types of clock are longer than the interrogatio n

between atoms and microwave, indicating that γ is in-

deed very small. However, in ce ll

[12,13]

or compact cold

atom clocks

[4−6]

, the co herent time of the atomic sample

is a main limitation in determining the duration of the

interrogation. Thus, γ must be considere d. A pulsed op-

tically pumped cell clock has been re po rted in a previous

1671-7694/2012/100201(4) 100201-1

 2012 Chinese Optics Letters

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