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Dynamic phase measurement of stored and retrieved light pulses

We demonstrated intuitively that the incoming and outgoing waves of stored light pulses are completely phase coherent, and dynamically measured phase evolution as a function of time for Gaussian pulses through the EIT sample. Phase is a manageable information carried by photons which can be employed as qubits or carriers of quantum information [1,2]. Highly dispersive media such as narrow atomic transitions and optical cavities are often considered as potential tools to manipulate the phase of light pulses [3,4]. In this paper, we describe a simple, direct, and dynamic method of the beat-note interferometer to measure the phase shift of light pulses induced by highly dispersive samples. With the method, we directly studied the phases of incoming and outgoing waves of stored light pulses; dynamically measured the phase as a function of time for Gaussian pulses through cold atoms under the condition of electromagnetically induced transparency (EIT) [5]. The beat-note interferometer is depicted in Fig. 1. In this system, a laser beam is passed through an acousto-optic modulator (AOM). The AOM’s zerothand first-order output beams are spatially recombined by a 50/50 beamsplitter (BS). The first-order beam probes the dispersive profile of the sample. The driving frequency, ωa, of the AOM is sufficiently large that interaction between the zeroth-order beam and the sample is negligible. The signals from PD1 and PD2 are proportional to Ez+Ef+2EzEf cos(ωat+φr) and Ez+Ef+2EzEf cos(ωat+φp+∆φ), where Ez and Ef are the amplitudes of the zerothand first-order beams. In our case, Ez is a constant and Ef is a slowly-varying function of time describing the envelope of a pulse. φr and φp are the phases that result from the optical paths from the AOM to BS or other factors. ∆φ is the phase shift induced by the sample. We measure ∆φ by comparing the two beat notes in the oscilloscope. Details of the above method can be found in Ref. [6]. We applied the beat-note interferometer to cold Rb atoms. Typically, 10 atoms are produced by the magneto-optical trap, as measured by the optical-pumping method [7]. The coupling and probe fields in the experiment drove the D2 transitions of |F=2〉 → |F'=2〉 and |F=1〉 → |F'=2〉, respectively. They formed the three-level Λ-type EIT configuration. Details of the two laser fields and the measured EIT spectrum can be found in Ref. [8]. The relaxation rate of the ground-state coherence in our system was about 0.002Γ, as estimated from the spectrum, where Γ= 2π×5.9 MHz is the spontaneous decay rate of the excited states. FIG. 1. The beat-note interferometer. M, mirror; BS, beamsplitter; PD, photodetector; OSC, oscilloscope. With the EIT effect, the probe pulse can be completely stopped in the atoms by switching off the coupling field, and subsequently released by the reverse process [9]. Figure 2(a) shows the data for a typical example of this intriguing ability to store and retrieve the probe pulse. The Rabi frequency of the coupling field is 0.35Γ and that of the peak of the probe pulse is 0.1Γ. Both the coupling and probe fields are tuned to their transition frequencies resonantly. The storage and retrieval of the probe pulse shown above is a coherent process [9,10]. This is demonstrated visually and intuitively in Fig. 2(b) with the beat-note interferometer. The black and red beat notes are the signals from PD1 and PD2, respectively. Data are averaged 256 times before recorded. If the phases of the incoming and outgoing waves of the storage were uncorrelated, the retrieved pulse could not show beat note due to the average. The phases in different parts of the probe pulse were quantitatively examined. Within the measurement accuracy, the phase of the retrieved wave perfectly evolves from the incoming wave and there is no observable phase jump caused by the switching process. We employed the beat-note interferometer to measure the phase shift as a function of time for QThL2-3