In future quantum communication systems, single photons, as the information carriers, are required to possess very narrow linewidths and accurate wavelengths for an efficient interaction with quantum memories. Spectral characterization of such single photon sources is necessary and must be performed with very high spectral resolution, wavelength accuracy and detection sensitivity. In this paper, we propose a method to precisely characterize spectral properties of narrow-linewidth single-photon sources using an atomic vapor cell based on electromagnetically-induced transparency (EIT). By using an atomic cesium vapor cell, we have experimentally demonstrated a spectral resolution of better than 150 kHz, an absolute wavelength accuracy of within 50 kHz and an exceptional detection sensitivity suitable for optical signals as weak as −117 dBm.
© 2017 Optical Society of America
Quantum memory is an essential device in the implementation of quantum repeaters and quantum computer networks. Currently, the main approaches to quantum memories are based on ions or atomic ensembles [1–9]. To integrate with these quantum memories, photonic qubits must have compatible wavelengths and linewidths. Except for a few approaches that work in the off-resonant range to achieve broad bandwidths, such as Raman, most quantum memory approaches work near atomic resonant transition lines and have a bandwidth in the order of MHz [10–17]. While most entangled photon sources are based on naturally broad (THz) spontaneous processes, such as spontaneous parametric down-conversion (SPDC) or spontaneous four wave mixing (SFWM), suitable linewidths for quantum memory integration have been implemented using extremely narrow filters [10, 11] or cavity enhancement [18–23].
To accurately characterize a ~MHz bandwidth source, the spectral resolution of the measuring instrument should have at least one order of magnitude better, i.e. ~100 kHz. This requirement is far beyond the ability of any gratings and etalons except for some type of very high-Q (greater than 109) cavity. It is still technically challenging to implement a high spectral stability cavity with such a high Q value. Therefore, the spectral measurement of single photons with linewidths of the order of MHz is extremely difficult for instruments based on traditional optical dispersive elements. Due to the lack of a suitable spectrometer, currently single photon linewidths are typically estimated indirectly from cavity lifetime measurements . The precise wavelength is uncertain and further tuning is required for integration with a quantum memory system. In addition, the spectral characterization of such sources requires single-photon level sensitivity.
In this paper, we propose a method to measure the spectra of narrow-linewidth single photons. The method is based on electromagnetically induced transparency (EIT) in an atomic vapor cell. It can provide high spectral resolution, high wavelength accuracy and high detection sensitivity for photons at a wavelength close to an atomic transition line. The spectral measurement range can be further extended beyond the immediate atomic transition lines by combining this method with the techniques of single-photon frequency conversion  and correlated biphoton spectroscopy . We have demonstrated this method with Cs atoms and experimentally studied its performance in terms of resolution, accuracy and sensitivity.
2. Principle and system configuration
EIT is the destructive interference of two light fields in a three-level atomic energy structure [27, 28]. The optical response of an atomic medium is modified when laser beams lead to quantum interference between the excitation pathways. This quantum interference can eliminate absorption and refraction (linear susceptibility) at the resonant frequency of the atomic transition .
In the lambda EIT configuration (in Fig. 1), the transition between the two lower energy states, |1〉 and |2〉, is dipole-forbidden and atoms can remain in either of the two states for a long time. Both energy states have allowed transitions to an excited state, |3〉. The optical fields that are resonant with the two allowed transitions of the atoms are absorbed by the atoms if they enter the atomic medium alone. However, when the two fields are applied to the atomic medium simultaneously, they interfere destructively, and therefore no atoms are excited to the state |3〉. Consequently, the field will not be absorbed.
A strong field between |1〉 and |3〉 is called the coupling field and a weak field between |1〉 and |2〉 is called the probe field. When the control beam is strong and its intensity is constant in time, the response of the atomic ensemble can be described in terms of the linear susceptibility spectrum , per Eq. (1):
In an ideal EIT medium, due to the dipole-forbidden transition between |1〉 and |2〉, the coherence relaxation rate is very small, i.e. →0. Based on Eq. (1), the linear susceptibility spectrum of the EIT medium for a signal beam is shown in Fig. 2. The linear response of an atom to the light can be described by the linear susceptibility . The imaginary part of determines the dissipation of the field by the atomic gas (i.e. absorption), while the real part of determines the refractive index. From Fig. 2(a), when = 0, the imaginary part of goes to zero, which indicates no absorption at the atomic resonance. In other words, the medium is transparent. The transparent frequency is determined by the frequency detuning of two optical fields and the transparency window is usually very narrow. Therefore, the spectrum of the probe light can be obtained by scanning the frequency of the coupling light.
2.2 System configuration
To accurately measure the spectrum and linewidth of single photons, we developed an experimental spectrometer based on EIT in a warm Cs atomic cell. The configuration of the spectrometer is shown in Fig. 3 (Box a). A tunable CW diode laser around 895 nm (Toptica DL100 pro) is locked to the Cs D1 transition 62S1/2 F = 3 → 62P1/2 F’ = 4. The beam was modulated by an acousto-optic modulator (AOM). The frequency of the first order diffraction output of the AOM is determined by Eq. (2):
The coupling beam is combined with the probe beam (the light under test) using a polarizing beam splitter (PBS) and is then sent into the Cs cell. The Cs cell is shielded in a 3-layer µ-metal chamber to block external stray magnetic fields. The vapor cell is heated by a temperature controller. After the beam passes through the cell, the coupling light is removed by a Glan-Thompson polarizer and a Fabry Perot (FP) Etalon. The probe light is transmitted and detected by a single-photon detector (PerkinElmer: SPCM-AQR-14). The output photon-count signal from the Si-APD is sent to the same computer. While the computer scans the RF signal (i.e. AOM driving frequency), it simultaneously collects the counts from the single photon detector. A spectrum based on the scanning frequency and corresponding photon counts is recorded and analyzed by a specifically built computer program.
To calibrate the spectrometer, we generated a probe field from the coupling light directly (Box b in Fig. 3). An electro-optic phase modulator (EOM) is used to generate sidebands at about a 9.2 GHz separation corresponding to the hyperfine splitting of the two ground states of Cs. An etalon selects the red-shifted sideband light, which corresponds to the transition 62S1/2 F = 4 → 62P1/2 F’ = 4. Another AOM is used to provide a similar detuning from the atomic transition and a variable optical attenuator is used to attenuate the light to single-photon level for system calibration. To experimentally study the performance of the spectrometer, we use another tunable laser (Newport TLB-6718-P) as an independent photon source (Box c in Fig. 3). Box d in Fig. 3 shows the energy structure for the experiment.
3. Experimental results and discussion
High spectral resolution is the main objective for this spectrometer. In our case, the spectral resolution is determined by the linewidth of the coupling field and the bandwidth of EIT transparent window. The linewidth of coupling field is determined by the laser linewidth, which is about 100 kHz in our experiment. The bandwidth of EIT transparent window for a Cs gas cell is influenced by the magnetic shield, cell temperature, coupling light power and angle between probe and coupling light. To ensure a narrow bandwidth, the cell is magnetically shielded by a 3-layer µ-metal chamber and the probe and coupling light are aligned in the same direction. The relationship between the bandwidth of EIT transparent window and coupling beam power and the cell temperature has been extensively studied. The full width half maximum (FWHM) of EIT bandwidth can be estimated by Eq. (3) [5, 29]:29, 30].
Although we can obtain a narrower bandwidth with lower intensity of coupling beam or higher cell temperature, there is a tradeoff between bandwidth and transmittance of EIT transparent window. The transmittance directly influences the spectrometer’s sensitivity. The output probe field intensity can be estimated by Eq. (4) [5, 29]:
A special calibration probe beam is generated (box b in Fig. 3) and then used to calibrate the EIT spectrometer. The calibration probe beam is a small portion split from the coupling beam and then shifted 9.2 GHz (the hyperfine splitting in the ground level), so any wavelength instability will not influence the measurement in the calibration procedure. Figure 4 shows the measured bandwidth of the EIT signal of the calibration probe beam as a function of coupling beam power and cell temperature. The bandwidth of the transparent window decreases with lower coupling beam intensity and higher temperature. When the coupling beam power is reduced to 0.7 mW, the bandwidth reaches approximately 120 kHz, which is already close to the linewidth of the laser beam itself. However, the transmittance is already low at such a power level. As a compromise between bandwidth and transmittance, we set the cell temperate to be 60 C and coupling beam power to be 1.3 mW. In this setting, we can get a resolution of approximately 150 kHz with a 40% transmittance at the center of the EIT window. The resolution and the transmittance can be optimized by varying the cell temperature or coupling beam power to accommodate a variety of measurements.
Because the spectrometer is designed to measure signals at a single-photon power level, its sensitivity is a critical performance parameter. The sensitivity is jointly limited by the transmittance, detection efficiency and noise.
Transmittance is determined by the transmittance of both the EIT transparent window and the filtering system. The transmittance of the EIT transparent window is determined by the coupling beam power and cell temperature. However, the higher the transmittance, the lower the spectral resolution. In our experiment, we balance the two parameters with a 150 kHz resolution and a 40% transmittance. The filtering system is designed to significantly suppress the coupling beam, but it also causes losses in the probe beam. The measured transmittance of the filtering system for the probe beam is approximately 80%. The detection efficiency of the single photon detector is approximately 38% near 895 nm. Therefore, the overall efficiency is approximately 12%.
The noise of the spectrometer is mainly due to three factors: the intrinsic dark counts of the single photon detector, fluorescence photons generated in the cell and residual photons from coupling beam. The intrinsic dark count rate is a constant, approximately 100 counts per second in our case. The fluorescence in the cell is mainly caused by collisions between atoms and collisions between the atoms and the cell wall. A buffer-gas-free and paraffin-coated cell can reduce the collision-induced fluorescence , and this kind of cell is used in this experiment. In the spectrometer, a strong coupling beam comes out of the cell together with the weak probe beam at a single-photon power level. The residual coupling beam becomes a significant source of noise in the system. Since the two beams should propagate collinearly through the cell to achieve an optimal resolution, a spatial filter is not suitable. Therefore, only polarization and spectral filters can be used to suppress the coupling beam. A Glan-Thompson polarizer is used as the polarization filter providing more than a 60-dB extinction in our experiment. For spectral filtering, since the frequency separation between the probe and the coupling beams is small (only 9.2 GHz in our experiment), it is not feasible to use dispersion-based spectral filters. Custom designed FP etalons are used as spectral filters in this experiment. The FP etalon is designed with a free spectral range of 18.4 GHz (9.2 GHz x 2) and a finesse of 17, which optimizes the extinction ratio of the transmittance for the probe to the coupling beams. Two FP etalons in series can provide more than 40 dB suppression to the coupling beam and approximately 80% transmittance for the probe beam. Combining the polarization filter and spectral filters, the coupling beams is suppressed by over 100 dB.
These noise sources are spectrally independent and nearly constant within the measurement range. Therefore, noise can be measured separately, and easily subtracted from the measurement results. Figure 5(a) shows a measured result and a corresponding measured background noise under the same conditions. Figure 5(b) shows a clean result after the background noise is subtracted. In this case, the measurement sensitivity is limited only by the noise deviation.
The spectrometer sensitivity is jointly limited by the detection efficiency and the deviation of noise. The noise counts have a shot noise behavior whose deviation is equal to the square root of the average number of counts. The noise count rate in the measurement range is approximately 20000 counts per second, so the noise count deviation is approximately 140 counts per second. Because we need to perform measurements two times (one for signal and another for background), the total noise deviation after subtracting the background noise is approximately 280 counts per second. To get a clear spectrum, the signal counts should be 5 times greater than the deviation. When we take the total efficiency of 12% into account, the spectrometer can measure signals as week as approximately 11000 photons per second (or −117 dBm at 895 nm). We attenuated the optical signal from the tunable laser under test to −105 dBm, −110 dBm and −115 dBm, and their spectrum measurement results are shown in Fig. 6. The results show the spectrum peak of the −115 dBm optical signal is clearly above the noise deviation level. It is worth pointing out that current superconducting single photon detectors [32, 33], such as supercomputing nanowire single-photon detectors or superconducting transition-edge sensor detectors, can achieve close to 100% detection efficiency and a lower dark count rate compared to the Si-APD. If such type of single photon detector replaced the Si-APD in this set-up, the spectrometer sensitivity may be further enhanced by about a factor of three.
Wavelength accuracy of the spectrometer is determined by the wavelength accuracy of the coupling beam. The coupling beam is from a diode laser and shifted by an AOM. The frequency shift of the AOM is controlled by a function generator, which has Hz level accuracy. Therefore, the accuracy is primarily determined by the wavelength accuracy of the coupling beam laser. The laser wavelength is locked to the peak of Doppler free hyperfine line of 62S1/2 F = 4 → 62P1/2 F’ = 4 transition based on Cs atom absorption saturation spectroscopy. The bandwidth of the natural line width of Cs D1 line (Doppler free hyperfine line) is approximately 5 MHz. With suitable parameters in Pound-Drever-Hall and proportional-integral-differential control settings, the wavelength can be accurately locked to within 1% of the bandwidth of the natural linewidth. Therefore, the wavelength reading of the spectrometer can be calibrated by the Doppler free hyperfine line of Cs atoms with an accuracy of better than 50 kHz.
The direct measurement range of this EIT spectrometer is limited to the absorption area around the atomic transitions, where the EIT can be observed. The Doppler broadened absorption range is temperature dependent, and is a few hundred MHz for Cs atom. The spectrum of single-photon sources in this range can be characterized directly using this approach. Single photon sources whose wavelength is not close to a suitable atomic transition line can be frequency-converted to this wavelength range and then measured using this approach. Since single photon frequency conversion was first proposed in 1990 , many groups have successfully demonstrated single photon frequency conversion using nonlinear optical processes, such as sum-frequency generation in bulk and waveguided periodically-poled lithium niobate and four-wave mixing in fiber [25, 35–44]. A number of research papers have reported single photon conversion from telecom wavelength (around 1550 nm or 1310 nm) to atomic transition wavelengths [17, 45–47]. It has been demonstrated that the quantum states of these photons are preserved during the conversion process. The wavelength of the converted photons is dependent on the wavelengths of both the original photon and the pump light. Therefore, using a narrow-linewidth and wavelength-stable pump laser, the spectral information of the original photon source can be obtained by measuring the converted photon. Such a frequency conversion based spectrometer has been demonstrated to measure the spectrum in the infrared range [48, 49]. The same technology can also extend the measurement range of this EIT-based spectrometer to other wavelengths, such as the telecom region. Moreover, correlated biphoton spectroscopy [26, 50–53] is another method for extending the measurement wavelength range. Correlated biphoton spectroscopy is a technique used to measure the spectral characteristics of an object, such as an optical filter or an absorber, by monitoring the coincidence counts from correlated signal and idler photon pairs generated by SPDC. Like frequency-conversion technology, if the pump wavelength in correlated biphoton spectroscopy is stable and has a narrow linewidth, an accurate spectral measurement of single photons in one beam can be obtained by measuring its correlated twin photons in another beam. In previous work , we have generated signal photons at a telecom (near 1310 nm) wavelength and idler photons at an atomic (cesium near 895 nm) transition wavelength. By applying the EIT spectrometer for the spectral measurement of 895 nm photons, the 1310 nm telecom spectrum can be obtained by coincidence counting. In summary, although the direct measurement range of the EIT spectrometer is limited to the narrow EIT transparent window around atomic transitions, single photon frequency conversion and correlated biphoton spectroscopy technologies can extend the technology to any other wavelength ranges while maintaining the performance of the EIT spectrometer, including its high spectral resolution, high wavelength accuracy and high detection sensitivity.
4. Conclusion experimental results and discussion
For a single photon source to efficiently interact with quantum memories, we must first characterize its spectral properties including wavelength and linewidth using a very sensitive instrument. Based on the principle of electromagnetically-induced transparency (EIT), we have proposed and demonstrated a method to precisely characterize the spectral properties of narrow-linewidth single-photon sources using an atomic vapor cell. The method is suitable for spectrum measurement of narrow linewidth weak optical signals, such as for the characterization of the narrow linewidth single photon sources for quantum memories. By using a Cs atomic vapor cell and Si-APD, we experimentally demonstrated this method with a spectral resolution of better than 150 kHz, a wavelength reading that is accurate to within 50 kHz and a sensitivity suitable for optical signals as weak as −117 dBm. By using superconducting single photon detectors, the sensitivity can be increased further. This method is demonstrated with Cs atoms, but it can also be applied to other atomic systems commonly used as storage media for quantum memories, such as Rubidium. In addition, by integrating single-photon frequency conversion or correlated biphoton spectroscopy, this technology can also be used for the characterization of single-photon sources at wavelengths that are not close to resonant transitions in atoms. The identification of any commercial product or trade name does not imply endorsement or recommendation by the National Institute of Standards and Technology.
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