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Time-Resolved Two-Photon Interference of Weak Coherent Pulses

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Time-Resolved Two-Photon Interference of Weak Coherent Pulses 1 Time-resolved two-photon interference of weak coherent pulses Heonoh Kim,1 Osung Kwon,2,a) and Han Seb Moon,1,a) 1Department of Physics, Pusan National University, Geumjeong-Gu, Busan 46241, Korea 2Affiliated Institute of Electronics and Telecommunications Research Institute, Daejeon 34044, South Korea a)Authors to whom correspondence should be addressed: [email protected] and [email protected] The observation of the Hong-Ou-Mandel (HOM)-type two-photon interference (TPI) has played an important role in the development of photonic quantum technologies. The time-resolved coincidence-detection technique has been effectively used to identify and characterize the TPI phenomena of long-coherence optical fields. Here, we report on the experimental demonstration of the TPI of two phase-randomized weak coherent pulses with time-resolved coincidence detection. The mutual coherence time between the two weak coherent lights is determined by applying a frequency noise to one of the two interfering lights. We analyze the HOM-type TPI-fringe visibility according to the ratio of the coherence time to the pulse duration. The interference of light from classical light or single- measurement has been employed to characterize the TPI photon sources lies at the heart of photonic quantum of long-coherence continuous-mode weak coherent lights information technologies [1-4]. In particular, the [17,18]. observation of the two-photon interference (TPI) of two To date, the time-resolved measurement of the TPI independent phase-randomized weak coherent pulses effect of two phase-independent pulse-mode photons has prepared in a single-photon level has played a key role in been commonly utilized to verify indistinguishability the practical realization of quantum communication between single photons generated from quantum systems protocols like measurement-device-independent quantum such as the atom-cavity system [15], quantum dots [19], key distribution (MDI-QKD) [5-12]. The most important and nitrogen-vacancy centers [20], organic dye molecule aspect in the successful implementation of the MDI-QKD [21], as well as from two highly different light sources at protocol is the observation of a high-visibility Hong-Ou- the single-photon level [22]. Mandel (HOM) fringe [13]. The TPI visibility can be When the two photons are overlapped temporally within strongly affected by intrinsic distinguishability factors the pulse duration, the TPI effect can be identified as a such as the frequency and polarization between the two reduction in the integrated coincidence counting events interfering photons, which can be quantified by the degree [15,19-22]. Therefore, the characteristic interference of mutual coherence between the photons. fringe reveals different shape upon varying the mutual The usual approach to observe the HOM interference coherence time between the two interfering photons. The fringe is to overlap two indistinguishable photons at a time-resolved TPI measurement can also be a useful tool beam splitter within their coherence time, which is to analyze the effects of mutual coherence between two significantly shorter than the timing resolution of the interfering weak coherent lights with very long coherence employed single-photon detectors (SPDs). Therefore, the times on the TPI fringe visibility [8]. characteristic HOM fringe shape is observed as a In this paper, we apply the time-resolved two-photon coincidence dip corresponding to the function of the detection technique to observe the characteristic TPI fringe arrival-time difference or relative optical delay between shape of phase-randomized pulse-mode weak coherent the two photons at the beam splitter [12,13]. lights. The mutual coherence time of the two interfering However, on employing a light source with a very long weak coherent lights is determined by observing the HOM coherence time relative to the time resolution of the SPDs, fringe when a frequency noise is applied to one of the two it is very difficult to implement the optical-delay interfering lights. The characteristic TPI fringe patterns based observation of the TPI full-fringe shape, whereas depending on the mutual coherence time are observed the time-resolved two-photon detection technique can be within a fixed pulse duration. We investigate the TPI effectively utilized to observe and characterize the TPI fringe visibility observed upon varying the ratio of the effect [14,15]. Particularly, we note that the time-resolved mutual coherence time to the pulse duration. Furthermore, coincidence-counting approach was initially used to we show that the conventional HOM-dip fringe shape can analyze the temporal distribution of pseudo-thermal light be obtained from the measured time-resolved TPI fringe source [16]. Recently, the time-resolved coincidence by bounding the coincidence time window. This approach 2 provides a comprehensive understanding of the TPI fringe Tp P t; dt shape measured using time-resolved two-photon detection T V 1.p (3) via its comparison with the conventional HOM-dip fringe Tp for photons with very short coherence times. P t; dt Tp In the case where pulse-mode phase-randomized weak Consequently, the TPI-fringe visibility can be expressed as coherent lights are employed to observe the TPI effect 11 based on time-resolved coincidence counting, the shape of VV1 22 exp 2 erf , (4) m 2 the cross-correlation histogram obtained by coincidence counting with two SPDs is given by the convolution of the where denotes the ratio of the coherence time to the pulse two input pulse shapes. Therefore, for two identical duration (TT/ ). From Eq. (4) we can estimate the upper bound square-shaped pulses with orthogonal polarizations, the cp time-dependent cross-correlation function affords the to obtain the TPI-fringe visibility according to the value of triangular-shaped histogram as per the following equation:. (or TTpc/ ). Interestingly, if we employ Gaussian- t shaped input pulses, the TPI-fringe visibility is given by Pt ; 1 , (1) 22 Tp Vm /1 ; however, the visibility exhibits a tendency where t denotes the detection-time difference between the two very similar to that expressed by Eq. (4). input photons at the SPDs and Tp is the full-width at half Figure 1 shows the schematic of our experiment to observe the maximum (FWHM) of the pulse duration. Eq. (1) corresponds to TPI of the two phase-randomized weak coherent pulses. the case where the TPI does not occur, and thus, it represents the Narrow-linewidth continuous-wave (CW) mode coherent light is convolved input pulse shape. emitted from a wavelength-tunable diode laser (New Focus, On the other hand, for the two input pulses with parallel Velocity TLB-6312, frequency of <300 kHz and wavelength polarizations, the cross-correlation function can be expressed as tuning range of 776 ~ 781 nm), which is strongly attenuated to the single-photon level by an optical attenuator consisting of t t2 P t; 1 1 Vm exp , (2) multiple stacked neutral density filters. The resulting linearly T T 2 p c polarized weak coherent light is then coupled to a polarization- where Tc denotes the half-width at 1/e maximum of the mutual maintaining single-mode fiber for matching the polarization orientation with the fiber-based modulators and polarization- coherence time of the two input pulses and Vm is the maximum based Mach-Zehnder interferometer. In the experiment, the visibility for TT. Under ideal conditions, is cp intensity modulator (IM: EOSPACE) is used only for pulse- estimated as 0.5 for weak coherent lights [23,24]. Now, Eq. (2) mode operation, which is performed at the input port of the corresponds to the case where TPI occurs, and thus, it represents interferometer to prepare the identical pulses contributing to the the characteristic TPI fringe shape obtained with phase- TPI. randomized pulse-mode weak coherent lights. Here, we assume the Gaussian-shaped mutual coherence function. The first term on the right-hand side of Eq. (2) corresponds to the convolved pulse shape in Eq. (1) thereby restricting the temporal range of coincidence counting; on the other hand, the second term represents the TPI fringe revealed within the pulse duration. It is noteworthy that Eq. (2) has the same form as that of the HOM-type TPI fringe measured as a function of the arrival-time difference t : N t N1 V exp 22 t , where N c c represents the measured coincidence, N the coincidences for tTc , V the TPI-fringe visibility, and the Gaussian- Fig. 1. Experimental setup to observe the two-photon shaped spectral bandwidth. Consequently, the first term in Eq. (2) interference of two phase-randomized weak coherent is analogous to the total coincidences within the resolving time pulses. IS: optical isolator, A: attenuator, P: linear (TR ) for continuous-mode coherent lights with a very short polarizer, FC: single-mode fiber coupler, IM: intensity modulator, H: half-wave plate, PBS: polarizing beam- coherence time (TTcR). splitter, PM: phase modulator, D: single-photon detector, The TPI-fringe visibility is defined using the two integrated TCSPC: time-correlated single-photon counter. coincidence counting distributions from Eqs. (1) and (2) as follows: 3 For the HOM two-photon interferometer employing two First, we performed the time-resolved measurement of the phase-randomized weak coherent lights, we use a polarization- HOM fringes by employing phase-randomized CW-mode weak based interferometer that consists of two half-wave plates (H1 coherent lights. In this case, in order to determine the mutual and H2) and three polarizing beam-splitters (PBS1, PBS2, and coherence time of the two interfering photons, we utilized the PBS3) as shown in Fig. 1. One half-wave plate H1 (with its axis PM without operating the IM. The time-resolved TPI fringes are oriented at 22.5°) is used to divide equally the input polarization measured for three different values of the frequency noise into the two paths of the interferometer by PBS1.
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