Hong–Ou–Mandel interference of two independent continuous-wave coherent photons Download: 672次
1. INTRODUCTION
The phenomenon of interference and its observation have been the focus of research in natural science and technology development for a long time. In particular, interference of individual particles such as atoms [1], electrons [2], neutrons [3], molecules [4], and photons [5] has played an essential role in our understanding of the superposition principle and wave-particle duality in quantum mechanics. In this context, we begin with Dirac’s famous statement on photon interference: “Each photon then interferes only with itself. Interference between different photons never occurs.” [6] Based on this idea, many experimental and theoretical studies have been undertaken to investigate the interference between two independent light sources [7
Meanwhile, since the early 1960s, Leonard Mandel’s pioneering research on the interference between two independent light sources that are strongly attenuated to the single-photon level has provided a starting point for new experimental perspectives on the interference of independent photons. Many of these experiments were performed utilizing photon counting and correlation techniques [15–
The most interesting and important two-photon interference experiment employing two identical photons from SPDC was reported by Hong, Ou, and Mandel (the HOM effect) [22]. The physics underlying the HOM effect includes both the two-photon analogy of Dirac’s statement on one-photon interference [6] and the quantum mechanical interpretation based on the interference between two alternative two-photon probability amplitudes [9,22,23]. Recently, observation of the HOM effect with identical (or indistinguishable) photons or entangled photons has played an important role in the practical implementation of photonic quantum information technologies [2426" target="_self" style="display: inline;">–
Meanwhile, Ou et al. performed the first HOM experiments with low-coherence classical light source for determining the second-order coherence time of a light beam based on the intensity-correlation technique [34]; this method has also been employed to measure the coherence time and pulse width of ultrafast pulses [35]. Recently, the two-photon interference experiments using classical light sources were extensively performed by Liu et al. with two dissimilar photon sources [36,37] and especially with two independent lasers [38,39]. In addition, HOM experiments with two fully independent coherent light sources have also played a key role toward practical implementation of the measurement-device-independent quantum key distribution (MDI-QKD) protocol [40
To date, most HOM experiments with two independent coherent light sources were performed under pulse-mode operation [40
In this paper, we experimentally demonstrate time-resolved HOM interference by employing two completely independent continuous-wave coherent photons (CWCPs) that are neither synchronized nor share any common reference. We used two external-cavity diode lasers (ECDLs) as narrowband coherent light sources and time-resolved measurements for two-photon coincidence counting. Furthermore, we employed two kinds of frequency-stabilization techniques using the spectra of atoms to prepare indistinguishable photons with higher coherence from the two locally separated ECDLs. Our frequency-stabilization technique utilizing high-resolution atomic spectroscopy can aid in the realization of long-distance quantum communication employing coherent light sources; this is because the approach guarantees the reference-free and absolute preparation of two fully independent coherent photons regardless of the separation distance between the light sources.
2. EXPERIMENTAL SETUP
Figure
Fig. 1. Experimental setup for observation of Hong–Ou–Mandel (HOM) interference with two completely independent continuous-wave coherent photons (CWCPs). (a) Schematic of the experimental setup for HOM interference between two independent CWCPs (P, polarizer; H, half-wave plate; Q, quarter-wave plate; BS, beam splitter; SPDs, single-photon detectors; TCSPC, time-correlated single-photon counter; Rb, atomic vapor cell of ; SAS, saturated absorption spectroscopy; PS, polarization spectroscopy). (b) SAS spectrum (blue curve) of ECDL1 and (c) PS spectrum (red curve) of ECDL2 for the transition of .
In our experiment, the two ECDLs are independently operated and spatially separated; therefore, the CWCP sources afford the advantages of their photons possessing an identical and high-frequency stability arising from frequency stabilization with respect to the hyperfine atomic transition line. The two CWCPs are coupled with two single-mode optical fibers (SMFs) to eliminate spatial-mode mismatch, and the two CWCPs are subsequently made incident on a 50:50 nonpolarizing beam splitter (BS). The polarizations of the two input photons are controlled by half (H)- and quarter (Q)-wave plates positioned at the two SMF input ports. After passage through the BS, the superposed output photons are detected by two SMF-coupled single-photon detectors (SPDs) (SPCM-AQRH-13-FC, Excelitas Technologies). The output signals from the two SPDs reach the time-correlated single-photon counter (TCSPC) for twofold coincidence counting and the subsequent time-resolved measurement of the HOM interference of the two independent CWCPs [49,50].
3. RESULTS
To observe a stable HOM interference fringe with two independent CWCPs, it is necessary to generate indistinguishable photons from two independent laser sources. Such indistinguishable independent CWCPs must exhibit identical spectral, spatial, and polarization modes at the two input ports of the BS. In particular, it is important to stably and accurately control the spectral properties of the two CWCPs via the application of a high-resolution frequency-stabilization technique. Therefore, in our work, we measured the mutual spectrum between the two coherent light sources by using the beat signal between the two ECDLs. With the setup shown in Fig.
Fig. 2. Spectral properties of two independent continuous-wave coherent photons. Spectral density spectrum of (a) frequency-stabilized ECDL1 upon error-signal locking of the SAS with frequency modulation and (b) frequency-stabilized ECDL2 obtained by offset locking of the PS.
When the two independent CWCPs with the spectral properties shown in Fig.
Fig. 3. Hong–Ou–Mandel interference fringe with two independent continuous-wave coherent photons. Experimental result and theoretical curve fitting under the conditions of a bandwidth of 3.3 MHz and .
Next, we changed the optical frequency of ECDL2 by adjusting the offset of the PS spectrum, as shown in Fig.
Fig. 4. Two-photon beat fringes for different offset frequencies. (a) PS spectra (blue: ; black: ; and red: ) of ECDL2 frequency-stabilized to the transition of ; the horizontal dashed line (gray) indicates the DC-offset reference. (b)–(d) The HOM-type two-photon beating fringes are measured for different offset frequencies.
We conducted a further experiment to verify that the time-resolved measurement of the HOM-type two-photon interference of the two fully independent and narrowband CWCPs is not affected by any temporal delay between the two interfering photons at the BS input ports. We repeated the measurements under the same experimental conditions as those applied for obtaining the HOM interference fringe shown in Fig.
Fig. 5. Hong–Ou–Mandel interference fringes with arbitrary time delay between two independent CWCP sources. Three single-mode fiber (SMF) spools are employed as relative optical delay lines (ODLs). (a) (black curve), (b) (red curve), (c) (green curve), and (d) (blue curve).
4. CONCLUSION
In conclusion, we successfully demonstrated HOM interference with weak coherent photons from two completely independent continuous-wave lasers without employing any synchronization mechanism between them. The indistinguishable CWCPs were stably generated with the use of high-resolution frequency stabilization that utilized frequency-locking to the hyperfine transition line of the atom. Our CWCP sources exhibit the advantages of possessing a universal identity and high-frequency stability, which guarantees the reference-free or absolute preparation of two independent and coherent photons regardless of the separation distance between the light sources. We believe that our approach can provide an efficient tool for the spectral characterization of light sources based on the two-photon interference of weak coherent light sources prepared by employing well-established high-resolution atomic spectroscopy. Moreover, the approach can be used to prepare indistinguishable coherent photons for the practical implementation of quantum communication systems.
Article Outline
Heonoh Kim, Danbi Kim, Jiho Park, Han Seb Moon. Hong–Ou–Mandel interference of two independent continuous-wave coherent photons[J]. Photonics Research, 2020, 8(9): 09001491.