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 between two ground states as signal to lock the local oscillator. The spectral width, signal-to-noise ratio (SNR), and contrast are the key factors determining clock performance. The width is directly related to the interaction 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 typical cesium beam clock has two microwave cavities separated by L, and a cesium beam passes through the cavities 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 of the cold atoms.The Ramsey fringe contrast is affected by decoherence during the evolution of atoms between two Ramsey pulses. Theoretically, however, contrast is not considered 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 received considerable attention due to their potential applications [4−7] . The compact cold atom clock has small volume, low weight, and high performance properties. 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 factor.Coherence during evolution is affected by several factors, 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 contrast resulting 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 |1 and |2 , respectively. The density matrix is expressed asThe hyperfine states that |1 and |2 have eigenvalues of E 1 and E 2 , respectively, and E 1 − E 2 = ω 0 , ω 0 is the hyperfine transition frequency between states |1 and |2 . The interaction between a two-level atom and a microwave field is described by the optical Bloch equations [10] given bywhere the perturbation term V 12 is expressed asand ω is the frequency of the microwave f...