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Abstract
Arbitrary shaping of optical waveform is fundamental interest from basic science to advanced optical technologies. However, it is still challenging task for shaping a biphoton wave packet. Here we experimentally manipulate the spectrum and phase of a biphoton wave packet in a two-dimensional frequency space. The spectrum is shaped by adjusting the temperature of the crystal, and the phase is controlled by tilting the dispersive glass plate. The manipulating effects are confirmed by measuring the two-photon spectral intensity (TSI) and the Hong-Ou-Mandel (HOM) interference patterns. The technique in this work paves the way for arbitrary shaping of a multi-photon wave packet in a quantum manner.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The ability to generate, manipulate and measure entangled photon pairs (biphotons) with an arbitrary time-frequency quantum state is of vital importance not only for developing a tool for practical quantum information and communication technologies, but also for conducting fundamental photonics studies [1]. Recently, the time-frequency duality of biphotons has been demonstrated by measuring two-photon spectral intensity (TSI) and two-photon temporal intensity (TTI) in the same condition [2], an important step for generating and measuring biphoton wave packets in a time-frequency domain. The manipulation of biphoton wave packets must be mastered before the arbitrary shaping of a biphoton wave packet in two-dimensional (2D) time-frequency space can be achieved. Especially, it is necessary to create multiple frequency modes in a 2D frequency space and to control the relative phases between the frequency modes [3].
Many previous works have been dedicated to the manipulation of the spectrum and phase of a biphoton wave packet. For narrow-band biphotons generated from a four-wave-mixing (FWM) process in a cold atomic ensemble within a magneto-optical trap (MOT), the biphoton temporal-spectral distribution is shaped by modulating the pump lasers using electro-optical modulators (EOM) [4], by using a spatial light modulator (SLM) [5], or by manipulating the dispersive properties of the electromagnetically induced transparency medium [6]. For biphotons generated from a spontaneous parametric downconversion (SPDC) process in a nonlinear crystal, the shaping of the wavepacket has been realized by several methods [7–15]. For example, Valencia et al. controlled the joint spectra of biphotons by spatially shaping the pump beam using a hologram [11]; Mittal et al. magnified biphoton’s temporal distribution using a time lens composed of dispersion fibers, EOM and gratings [12]; Matsuda shaped biphotons using cross-phase modulations with a photonic crystal fiber (PCF) [13]; and the spectra and phases of biphotons can also be manipulated using SLM [14,15].
Although the previous schemes [4–15] have provided several effective ways to modulate biphotons, these techniques rely on preexisting technologies to modulate the constituent photons of a biphoton wave packet. In this work, we propose and demonstrate a new approach to jointly modulate a biphoton wave packet. The spectra of the biphotons are shaped by simply adjusting the temperature of the crystal and the phase is adjusted just by tilting the angle of a glass plate. The shaping effect is confirmed by measuring the TSI and Hong-Ou-Mandel (HOM) [16] interference patterns.
2. Experiment and its theoretical model
The experimental scheme for the generation of an entangled photon source is shown in Fig. 1. The pump laser pulses pass through a nonlinear crystal (NLC), a dual-wavelength wave plate (DWP), and a dispersive medium (D) twice so as to generate an entangled state with spectrum of
Here, s(ω1, ω2) is the biphoton spectral amplitude generated when the pump passes though the type-II NLC; ω1 and ω2 are the angular frequencies of the down converted biphotons. ϕ is the phase difference between the first photon pair (generated by the first pass of the pump in the NLC) and the second photon pair (generated by the second pass of the pump in the NLC). ϕ is introduced by the dispersive medium, which has different chromatic dispersions for the pump and the downconverted daughter photons. ϕ can be continuously controlled by tilting the dispersive medium.
Fig. 1 Schematic of creation of a discrete-frequency entangled biphoton in bidirectional pump. NLC, nonlinear crystal; DWP, dual-wavelength wave plate; M, mirror; D, dispersive medium.
Note that the DWP works as a half-wave plate for the pump and a quarter-wave plate for the biphoton, and this method works only when the frequencies of down-converted photons are close. As a result of the passing of the DWP twice, the polarization of the pump pulse is not changed while the polarizations of the constituent photons of the biphoton are interchanged, i.e., s(ω1, ω2) is changed to s(ω2, ω1) [17, 18]. Further, the relative phase ϕ can maintain long-term stability against the disturbance, since the pump pulses propagate together with the biphotons between the NLC and the mirror M.
The real experimental setup is shown in Fig. 2(a)–2(c). Figure 2(a) is the setup for the entangled photon source based on the scheme in Fig. 1. Here, the group-velocity-matched (GVM) periodically poled KTiOPO4 (PPKTP) crystal is adopted as the NLC for type-II SPDC (y→ y + z), and ω1(2) is the angular frequency of the photons polarized aligned along the y- (z-) axis [19,20]. A glass plate is employed as the dispersion medium. The pump pulses from a mode-locked Ti:sapphire laser have a center wavelength of 792 nm and a bandwidth of approximately 0.2 nm (the corresponding temporal duration is approximately 4 ps) with a repetition rate of 76 MHz. Figure 2(b) is the setup for the two-photon spectral intensity (TSI) measurement, similar to what we used in [20,21]. Figure 2(c) shows the HOM interference measurement; more technical details can be found in [22,23].
Fig. 2 Experimental setup for (a) biphoton source, (b) TSI measurement, (c) HOM measurement. PPKTP has a length of 30 mm and a polling period of 46.2 μm. DWP, dual-wavelength wave plate; SMF, single-mode fiber; APD, avalanche photodiode; PBS, polarizing beam splitter; HWP, half-wave plate; TBPF, tunable bandpass filter; TIA, time interval analyzer.
In a HOM interference, the two-fold coincidence probability P as a function of optical path delay τ can be calculated as [23]
It can be assumed that the spectral functions s(ω1, ω2) and s(ω2, ω1) contain no imaginary part due to the constant phase distributions. So, we obtain the relation of relationship of S(ω2, ω1) = e iϕS*(ω1, ω2), where * denotes the complex operation. P(τ) can be further simplified as3. Results
First, we demonstrate the shaping of the biphoton spectrum by adjusting the temperature of the PPKTP crystal. Temperature is an important parameter for manipulating the spectra of biphotons from periodically poled crystals [24,25]. The effect of the shaping is confirmed by measuring the TSI and HOM interference. Figure 3(a) shows the measured TSI at 65 °C for PPKTP. Note that Δν1(2) in Fig. 3 is the shifted frequency for ω1(2) from the center frequency. Thanks to the GVM condition, the states s(ω1, ω2) and s(ω2, ω1) in Eq. (1) have round shapes in the TSI [26–30]. We project the TSI data onto the horizontal axis to obtain its marginal distribution, and the spectral period equals to the distance between the two peaks in the marginal distribution. The two frequency modes were separated by 0.40 THz in Fig. 3(a). When the temperature was increased to 80 °C in Fig. 3(b), the frequency separation was 0.61 THz. Figure 3(c) shows the HOM interference patterns at 65 °C with an interference visibility of 84.6±2.0% and a beating period of 2.3 ps. Here, the visibility is defined as (max−min)/(max+min). Higher visibilities in the HOM patterns guarantee the exchange symmetry of the two-photon spectral distribution. At 80 °C in Fig. 3(d), the interference visibility was 88.2±1.7%, comparable to that in Fig. 3(c), but the beating period decreased to 1.6 ps. The temporal period was shorter in Fig. 3(d) because the spectral period was enlarged in Fig. 3(b). The frequency separations in the TSI data are in good agreement with the beat frequencies in the HOM patterns, since Δυ = 1/Δτ, where Δυ is the separation of the spectral modes and Δτ is the beating period.
Fig. 3 Observed two-photon spectral intensities with normalization (upper) and their HOM interference patterns (lower). The plots on the left (right) show the data at the PPKTP temperature of 65 °C (80 °C). Error bars are equal to the square root of each data point by assuming Poissonian counting statistics. The solid line is the fitting of the experimental data.
Next, we demonstrate controlling the relative phase ϕ by tilting the glass plate. We fixed the temperature at 45 °C for the PPKTP with the measured TSI shown in Fig. 4(a). With a phase at ϕ = 0.0 π, the HOM interference pattern was symmetric as shown in Fig. 4(b), with a visibility of 83.6 ±2.9% and a beating period of 4.4 ps. When the phase was increased to 0.6 π, the HOM interference pattern was asymmetric, as shown in Fig. 4(c). The phase can be continuously increased, and Figs. 4(d)–4(e) show the case of ϕ = 1.1 π and 1.4 π. We obtained the phase value by fitting the experimental data. All the patterns in Fig. 4(b)–4(e) have the same period. Note, we measured coincidence counts in 6 sec. for Figs. 3(a)–3(b), and 5 sec. for Fig. 4(a). In these accumulation times, the maximum counts were 160, 203 and 175, respectively. We set the coincidence window of 3 ns for all the data.
Fig. 4 Demonstration of the controllability of the relative phase between the two spectral modes s(ω1, ω2) and s(ω2, ω1). (a) Normalized two-photon spectral intensity (TSI) at 45 °C for PPKTP. (b)–(e) Corresponding HOM interference patterns at different relative phases. Error bars assume Poissonian counting statistics. The solid line is the fitting of the experimental data.
4. Discussion
As shown in Fig. 3, we have created discrete frequency modes in a 2D frequency space. The separation between the two frequency modes can be controlled just by changing the crystal’s temperature. To the best of our knowledge, this is the first experimental demonstration of the relationship between the discrete frequency mode in the TSI and the HOM interference patterns.
With the data shown in Fig. 4, we have controlled the relative phase between two frequency modes by adjusting the tilting angle of the glass plate. This technique will be useful for future applications requiring precise control of the relative phase in a time-frequency entangled state. For the maximal controlling range of our technique, the spectral separation can reach 2.4 THz by heating the crystal from room temperature to 200 °C; by tilting the glass plate, the phase can be adjusted from 0 to 2 π.
The next step in our work is to verify the temporal shaping effect of a biphoton wave packet with the quantum manipulation technique, which has been presented in this study by measuring a two-photon temporal distribution. Our approach to time-frequency entangled photons may be useful for optical science and technologies. In particular, the technique for shaping a biphoton wave packet could be developed as quantum optical synthesis in a 2D time-frequency space, which might be a next-generation technology beyond the conventional optical synthesis carried out in 1D systems.
5. Conclusion
We have demonstrated joint manipulation of the biphoton spectrum and phase. The frequency separation can achieve 2.4 THz by changing the crystal temperature, and the phase can be adjusted by 2 π by tilting the angle of a glass plate. We have also experimentally demonstrated, for the first time, the correspondence between TSI and HOM interference with different spectra and phases. Our work opens up new possibilities for shaping entangled photons for various quantum optical and quantum information applications.
Funding
The National Natural Science Foundations of China (Grant Number 11704290 and 11104210); The fund from the Educational Department of Hubei Province, China (Grant Number D20161504); The JSPS KAKENHI (Grant Number JP17H01281); The Research Foundation for Opto-Science and Technology, Hamamatsu, Japan; The Matsuo Foundation, Tokyo, Japan.
References and links
1. Y. Shih, An introduction to quantum optics: photon and biphoton physics (CRC Press, 2011).
2. R.-B. Jin, T. Saito, and R. Shimizu, “Experimental demonstration of time-frequency duality of biphotons,” arXiv:180109044 (2018).
3. H.-S. Chan, Z.-M. Hsieh, W.-H. Liang, A. H. Kung, C.-K. Lee, C.-J. Lai, R.-P. Pan, and L.-H. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science 331, 1165 (2011). [CrossRef] [PubMed]
4. J. F. Chen, S. Zhang, H. Yan, M. M. T. Loy, G. K. L. Wong, and S. Du, “Shaping biphoton temporal waveforms with modulated classical fields,” Phys. Rev. Lett. 104, 183604 (2010). [CrossRef] [PubMed]
5. L. Zhao, X. Guo, Y. Sun, Y. Su, M. M. T. Loy, and S. Du, “Shaping the biphoton temporal waveform with spatial light modulation,” Phys. Rev. Lett. 115, 193601 (2015). [CrossRef] [PubMed]
6. Y.-W. Cho, K.-K. Park, J.-C. Lee, and Y.-H. Kim, “Engineering frequency-time quantum correlation of narrow-band biphotons from cold atoms,” Phys. Rev. Lett. 113, 063602 (2014). [CrossRef] [PubMed]
7. V. Torres-Company, A. Valencia, and J. P. Torres, “Tailoring the spectral coherence of heralded single photons,” Opt. Lett. 34, 1177–1179 (2009). [CrossRef] [PubMed]
8. N. Tischler, A. Büse, L. G. Helt, M. L. Juan, N. Piro, J. Ghosh, M. J. Steel, and G. Molina-Terriza, “Measurement and shaping of biphoton spectral wave functions,” Phys. Rev. Lett. 115, 193602 (2015). [CrossRef] [PubMed]
9. W.-M. Su, R. Chinnarasu, C.-H. Kuo, and C.-S. Chuu, “Shaping single photons and biphotons by inherent losses,” Phys. Rev. A 94, 033805 (2016). [CrossRef]
10. V. Ansari, E. Roccia, M. Santandrea, M. Doostdar, C. Eigner, L. Padberg, I. Gianani, M. Sbroscia, J. M. Donohue, L. Mancino, M. Barbieri, and C. Silberhorn, “Heralded generation of high-purity ultrashort single photons in programmable temporal shapes,” Opt. Express 26, 2764–2774 (2018). [CrossRef] [PubMed]
11. A. Valencia, A. Cere, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99, 243601 (2007). [CrossRef]
12. S. Mittal, V. V. Orre, A. Restelli, R. Salem, E. A. Goldschmidt, and M. Hafezi, “Temporal and spectral manipulations of correlated photons using a time lens,” Phys. Rev. A 96, 043807 (2017). [CrossRef]
13. N. Matsuda, “Deterministic reshaping of single-photon spectra using cross-phase modulation,” Sci. Adv. 2, e1501223 (2016). [CrossRef] [PubMed]
14. A. Pe’er, B. Dayan, A. A. Friesem, and Y. Silberberg, “Temporal shaping of entangled photons,” Phys. Rev. Lett. 94, 073601 (2005). [CrossRef]
15. C. Bernhard, B. Bessire, T. Feurer, and A. Stefanov, “Shaping frequency-entangled qudits,” Phys. Rev. A 88, 032322 (2013). [CrossRef]
16. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987). [CrossRef] [PubMed]
17. R.-B. Jin, R. Shimizu, K. Wakui, M. Fujiwara, T. Yamashita, S. Miki, H. Terai, Z. Wang, and M. Sasaki, “Pulsed Sagnac polarization-entangled photon source with a PPKTP crystal at telecom wavelength,” Opt. Express 22, 11498–11507 (2014). [CrossRef] [PubMed]
18. A. Paterova, S. Lung, D. A. Kalashnikov, and L. A. Krivitsky, “Nonlinear infrared spectroscopy free from spectral selection,” Sci. Rep. 7, 42608 (2017). [CrossRef] [PubMed]
19. F. König and F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO4 with zero group-velocity mismatch,” Appl. Phys. Lett. 84, 1644 (2004). [CrossRef]
20. R. Shimizu and K. Edamatsu, “High-flux and broadband biphoton sources with controlled frequency entanglement,” Opt. Express 17, 16385–16393 (2009). [CrossRef] [PubMed]
21. R.-B. Jin, R. Shimizu, K. Wakui, H. Benichi, and M. Sasaki, “Widely tunable single photon source with high purity at telecom wavelength,” Opt. Express 21, 10659–10666 (2013). [CrossRef] [PubMed]
22. N. S. Bisht and R. Shimizu, “Spectral properties of broadband biphotons generated from PPMgSLT under a type-II phase-matching condition,” J. Opt. Soc. Am. B 32, 550–554 (2015). [CrossRef]
23. R.-B. Jin and R. Shimizu, “Extended Wiener-Khinchin theorem for quantum spectral analysis,” Optica 5, 93–98 (2018). [CrossRef]
24. A. Fedrizzi, T. Herbst, M. Aspelmeyer, M. Barbieri, T. Jennewein, and A. Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New J. Phys. 11, 103052 (2009). [CrossRef]
25. Z.-Y. Zhou, S.-K. Liu, S.-L. Liu, Y.-H. Li, Y. Li, C. Yang, Z.-H. Xu, G.-C. Guo, and B.-S. Shi, “Revealing the behavior of photons in a birefringent interferometer,” Phys. Rev. Lett. 120, 263601 (2018). [CrossRef] [PubMed]
26. M. Yabuno, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Four-photon quantum interferometry at a telecom wavelength,” Phys. Rev. A 86, 010302 (2012). [CrossRef]
27. N. Bruno, A. Martin, T. Guerreiro, B. Sanguinetti, and R. T. Thew, “Pulsed source of spectrally uncorrelated and indistinguishable photons at telecom wavelengths,” Opt. Express 22, 17246–17253 (2014). [CrossRef] [PubMed]
28. R.-B. Jin, P. Zhao, P. Deng, and Q.-L. Wu, “Spectrally pure states at telecommunications wavelengths from periodically poled MTiOXO4 (M=K, Rb, Cs; X=P, As) crystals,” Phys. Rev. Appl. 6, 064017 (2016). [CrossRef]
29. R.-B. Jin, G.-Q. Chen, H. Jing, C. Ren, P. Zhao, R. Shimizu, and P.-X. Lu, “Monotonic quantum-to-classical transition enabled by positively correlated biphotons,” Phys. Rev. A 95, 062341 (2017). [CrossRef]
30. C. Greganti, P. Schiansky, I. A. Calafell, L. M. Procopio, L. A. Rozema, and P. Walther, “Tuning single-photon sources for telecom multi-photon experiments,” Opt. Express 26, 3286–3302 (2018). [CrossRef] [PubMed]
