Electromagnetically induced transparency in modulated laser fields

Transcription

1 Journal of Physics B: Atomic, Molecular and Optical Physics PAPER Electromagnetically induced transparency in modulated laser fields To cite this article: Yuechun Jiao et al J. Phys. B: At. Mol. Opt. Phys Manuscript version: Accepted Manuscript Accepted Manuscript is the version of the article accepted for publication including all changes made as a result of the peer review process, and which may also include the addition to the article by IOP Publishing of a header, an article ID, a cover sheet and/or an Accepted Manuscript watermark, but excluding any other editing, typesetting or other changes made by IOP Publishing and/or its licensors This Accepted Manuscript is IOP Publishing Ltd. During the embargo period (the month period from the publication of the Version of Record of this article), the Accepted Manuscript is fully protected by copyright and cannot be reused or reposted elsewhere. As the Version of Record of this article is going to be / has been published on a subscription basis, this Accepted Manuscript is available for reuse under a CC BY-NC-ND.0 licence after the month embargo period. After the embargo period, everyone is permitted to use copy and redistribute this article for non-commercial purposes only, provided that they adhere to all the terms of the licence Although reasonable endeavours have been taken to obtain all necessary permissions from third parties to include their copyrighted content within this article, their full citation and copyright line may not be present in this Accepted Manuscript version. Before using any content from this article, please refer to the Version of Record on IOPscience once published for full citation and copyright details, as permissions will likely be required. All third party content is fully copyright protected, unless specifically stated otherwise in the figure caption in the Version of Record. View the article online for updates and enhancements. This content was downloaded from IP address... on 0/0/ at 0:

2 Page of AUTHOR SUBMITTED MANUSCRIPT - JPHYSB-.R Electromagnetically induced transparency in modulated laser fields Yuechun Jiao,, Zhiwei Yang,, Hao Zhang,, Linjie Zhang,, Georg Raithel,, Jianming Zhao,, and Suotang Jia, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser spectroscopy, Shanxi University, Taiyuan 0000, P. R. China Department of Physics, University of Michigan, Ann Arbor, Michigan -,. Introduction USA Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 0000, China zhaojm@sxu.edu.cn Abstract. We study electromagnetically induced transparency (EIT) in a roomtemperature cesium vapor cell using wavelength-modulated probe laser light. In the utilized cascade level scheme, the probe laser drives the lower transition S / (F = ) P / (F = ), while the coupling laser drives the Rydberg transition P / S /. The probe laser has a fixed average frequency and is modulated at a frequency of a few khz, with a variable modulation amplitude in the range of tens of MHz. The probe transmission is measured as a function of the detuning of the coupling laser from the Rydberg resonance. The first-harmonic demodulated EIT signal has two peaks that are, in the case of large modulation amplitude, separated by the peak-to-peak modulation amplitude of the probe laser times a scaling factor λ p /λ c, where λ p and λ c are the probe- and coupling-laser wavelengths. The scaling factor is due to Doppler shifts in the EIT geometry. Second-harmonic demodulated EIT signals, obtained with small modulation amplitudes, yield spectral lines that are much narrower than corresponding lines in the modulation-free EIT spectra. The resultant spectroscopic resolution enhancement is conducive to improved measurements of radio-frequency (RF) fields based on Rydberg-atom EIT, an approach in which the response of Rydberg atoms to RF fields is exploited to characterize RF fields. Here, we employ wavelength modulation spectroscopy to reduce the uncertainty of atom-based frequency and field measurement of an RF field in the VHF radio band. Electromagnetically induced transparency (EIT) is a quantum interference effect between two excitation pathways driven by two laser fields within a three-level system []. Recently, cascade EIT involving Rydberg states with high principal quantum numbers, n, has attracted interest due to the high susceptibility of Rydberg atoms to external fields (scaling n ) and large microwave-transition dipole moments (scaling n ). Rydberg EIT spectra have been used to measure the electric fields Author to whom any correspondence should be addressed

3 AUTHOR SUBMITTED MANUSCRIPT - JPHYSB-.R Page of of electromagnetic (EM) radiation with a large dynamic range [], including radiofrequency (RF) [,, ] and millimeter waves [,,,, ]. However, in weak fields the RF-induced modifications of the EIT spectra are small, which limits the precision and accuracy of atom-based RF electric-field measurement. Wavelength / frequency modulation spectroscopy is widely used to enhance the sensitivity of spectroscopic measurements [] and can be used in high order for weaksignal detection [, ]. In the present work we first explore the response of EIT spectra to modulation of the laser light, a scheme that is complementary to modulating the Rydberg levels with an applied RF field [,, ]. We present the signatures of frequency modulation of the probe-laser field in the Rydberg-EIT scheme, measured with a cesium room-temperature vapor cell. The probe laser is frequency-modulated over a range of several tens of MHz, at modulation frequencies ranging from to khz. The probelaser transmission is recorded as a function of the detuning of the coupling laser from resonance. The demodulated EIT signal is independent of the modulation frequency and exhibits a characteristic shape with two peaks at a separation proportional to the probe-laser modulation amplitude. We then apply wavelength modulation spectroscopy to improve atom-based measurements of the field strength and the frequency of an RF field applied to the spectroscopic cell.. Experimental setup The experiments are performed in a cesium cascade three-level system consisting of the ground state S /, F = ( g ), the intermediate state P / F = ( e ) and a ns / Rydberg state ( r ). The strong coupling laser, λ c, drives the Rydberg transition e r = S /. The transmission of the weak probe laser, λ p, which is resonant with the lower transition g e, is detected with a photodiode (PD). The coupling-laser (Toptica TA-SHG, linewidth MHz, /e radius w 0 = µm and Rabi frequency Ω c = π. MHz) and the probe-laser beam (Toptica DL0, /e radius µm and Ω p = π. MHz) are counterpropagated through a 0-mm long cesium vapor cell held at room temperature. A schematic of the experimental setup and the relevant energy levels are shown in Fig.. The EIT signal is measured by scanning the coupling laser through the Rydberg transition, while the probe laser is locked to the g e transition. Further, in order to frequency-modulate the probe, the probe-laser current is modulated with a function generator (FG) with a modulation frequency ω, as shown in Fig. (a). The EIT signal is modulated due to the current/frequency modulation of the probe laser. We obtain the demodulated EIT signal using a lock-in amplifier (SR0). The demodulated signals shown are modulation amplitudes in the PD current (R-output or X-output of the SR0) at the first and second harmonic of the wavelength modulation frequency.

4 Page of AUTHOR SUBMITTED MANUSCRIPT - JPHYSB-.R (a) PD Input Coupling Laser DM nm R(X)-Output SAS Locking SR0 Lock-in Amplifier REF IN nm Probe Laser DM (b) / PBS Block Figure. (Color online) (a) Schematic of the experimental setup. The coupling laser ( nm) and the probe laser ( nm) counterpropagate through a cesium vapor cell. The probe laser is locked using saturated absorption spectroscopy (SAS) and is current-modulated with a function generator (FG). The probe beam passes through a dichromatic mirror (DM), and its transmission is detected using a photodiode detector (PD). The EIT signal from the PD is demodulated using a lock-in amplifier. (b) Energy levels of the utilized cascade system. The ground and intermediate states, g = S /, F =, m F and e = P /, F =, m F, are driven by a weak probe field (lower transition), while the upper e r = S / transition is driven by a strong coupling field. The transmission on the lower transition, g e, shows an EIT transmission peak when both the lower (probe) and the upper (coupling) transitions are resonant.. EIT spectra in modulated laser fields As shown in Fig. (b), the coupling and probe lasers drive resonant or near-resonant transitions g e r, with above Rabi frequencies Ω c and Ω p, thereby forming a cascade EIT system. The coupling transition modifies the refractive and absorptive properties of the medium for probe frequencies near the g e transition. The modifications due to the strong coupling field, including the EIT transparency windows, are observed using a weak probe laser []. In the EIT regime, it is Γ Ω c Ω p, with intermediate-state decay rate Γ = π. MHz. In our work, the probe laser is modulated and the coupling laser is scanned, and the demodulated EIT spectra are measured versus coupling-laser frequency. Due to the current modulation of the probe laser, the probe-laser detuning from the g e transition follows a time dependence p (t) = p0 sin(ωt), with a modulation frequency ω and amplitude p0 > 0. Defining the probe-beam direction as x, the velocity class v x and the coupling-laser detuning c at which the EIT-condition (i.e. resonance on both the probe and the coupling transitions) occurs are given by v x = λ p p /(π) c p Output r e g FG

5 AUTHOR SUBMITTED MANUSCRIPT - JPHYSB-.R Page of c = λ p p = ξ scale p. () λ c The factor ξ scale = λ p /λ c, which originates in the different Doppler shifts of probe and coupling beams, depends on the atomic species and the transitions used. In this work ξ scale =.. The magnitude R and the X-quadrature component of the demodulated EIT signal are given by π/ω S R,demod ( c ) = ω exp(iqωt)t [ c + c0 sin(ωt)]dt () t=0 π/ω S X,demod ( c ) = ω cos(qωt)t [ c + c0 sin(ωt)]dt () t=0 with the modulation-free EIT signal function T ( c ). We obtain the demodulated signals for orders q = and q = using the lock-in amplifier (the q = and q = orders are offered by most lock-in amplifiers). S demod (arb. units) p0 / =. MHz c p0 / =.0 MHz p0 / = 0.0 MHz / =. MHz c / =.0 MHz c / (MHz) Figure. (Color online) Bottom curve: Experimental EIT signal T E ( c ) for unmodulated probe laser (black solid line), obtained by scanning the coupling laser across the e r resonance, with Gaussian (red dashed line) and Lorentzian (green thin lines) fits. For clarity, the fits are offset in vertical direction. Top curves: Demodulated EIT spectra S R,demod ( c ) (black solid lines) for the indicated modulation amplitudes, p0, and ω = π khz, and demodulation order q =. The fit results are obtained with Eq. using T E ( c ) (blue dotted lines), the Gaussian fit to T E ( c ) (red dashed lines; vertically offset), or the Lorentzian fit to T E ( c ) (green thin lines; vertically offset). In the following we present measurements of S R,demod ( c ), as introduced in Eq., using the cascade Rydberg energy level scheme, shown in Fig. (b) with r = S /.

6 Page of AUTHOR SUBMITTED MANUSCRIPT - JPHYSB-.R In Fig., we show the measured modulation-free EIT signal, T E ( c ) (bottom curve) and demodulated EIT spectra, S R,demod ( c ) (top and middle) for modulation frequency ω = π khz, demodulation order q =, and the indicated modulation amplitudes. The linewidth of the modulation-free EIT transmission signal, T E ( c ) in Fig., is measured to be about π. MHz, which is close to the theoretical lower limit of Ω c/γ (Γ is the decay rate of the P / level). As expected from Eq., S R,demod ( c ) exhibits two peaks for all non-zero values of p0. The probe modulation amplitudes for the top and middle curves are p0 = π. MHz and.0 MHz, respectively, and the gaps between the two signal peaks are measured to be π. MHz and.0 MHz ( i.e. close to the expected values ξ scale p0 ). Using T E ( c ) for T ( c ) in Eq. and varying c0, we obtain model signals [blue dotted lines in Fig. ] that agree very well with the measured data [black lines in Fig. ]. The fit results for p0 = c0 /ξ scale are π.0 MHz and. MHz; these values are close to the actually applied values of p0 = π. MHz and.0 MHz. Half Peak Splitting in c/ (MHz) S R,demod scale x p0 khz khz khz p0/ (MHz) Figure. (Color online) Half-spacings between the peaks in demodulated EIT signals (symbols) measured for r = S / and for the indicated modulation frequencies as a function of the modulation amplitude of probe laser, p0. The demodulation order q =. We also show the half-spacings between the peaks in calculations of S R,demod based on Eq. (solid line). Linear fits to the experimental data return slopes of.,.0, and., for modulation frequencies ω = π khz, khz, and khz, respectively. The average measured slope of. (short-dashed line) is in excellent agreement with the calculation. For comparison, we have used alternate models in which we first fit T E ( c ) [lowest curve in Fig. ] with a Gaussian (red dashed line) and a Lorentzian (green line) function. The fit results, denoted T G ( c ) and T L ( c ), have FWHM of π. MHz and. MHz. The top pair of experimental curves in Fig. have then been fitted using Eq., with T G ( c ) or T L ( c ) for the EIT response function [instead of T E ( c )]. The results obtained with T G ( c ), shown as red dashed lines in Fig., also fit the experimental

7 AUTHOR SUBMITTED MANUSCRIPT - JPHYSB-.R Page of data very well and are near-indistinguishable from the fits based on T E ( c ). The results obtained with T L ( c ), shown as green thin lines, fit less well due to the wide wings of the Lorentzian function, which the experimental EIT response function does not have. While the quality of the fits varies slightly with the fitting model used, the fit results for p0 = c0 /ξ scale in Eq. are stable. For the case of the upper two curves in Fig., the fit results for p0 vary by π 0. MHz for all fitting models. (a) / (MHz ) (b) p0 S R,demod (arb. units) MHz.0 MHz. MHz p0 / =. MHz p0 / =.0 MHz p0 / =.0 MHz c / (MHz) Figure. (Color online) (a) Calculations of demodulated EIT signals S R,demod ( c ) with q = from Eq., using a Gaussian response function T G ( c ) with FWHM = MHz. (b) Measurements with the indicated probe laser modulation amplitudes, p0, for modulation frequency khz. We have performed sets of similar measurements with different modulation frequencies. In Fig., we present half the measured spacings of the peaks in S R,demod ( c ) as a function of probe modulation amplitude, p0, for modulation frequencies of ω = π khz, khz, and khz. We observe a linear dependence of the spacings on the probe modulation amplitude, with a slope that approaches ξ scale =. and is independent of the modulation frequency. These observations agree well with calculations based on Eqs. -. The demodulated signal in Eq. allows further characterization by using higher orders (integers q > ). The q = demodulated signal is obtained by selecting the f output of our (and most other) lock-in amplifiers. In Figure we present several measurements and corresponding calculations of S R,demod ( c ) for q =. Experimental and calculated results are in excellent agreement with each other. Further, the higherorder demodulated signals exhibit additional structure and sharper features than the q = signals; this can be used to achieve improved spectroscopic resolution of atomic transitions [, ]. The larger probe laser modulations employed in Figs. and are useful for a complete characterization of the modulation method. For weak-signal detection, the probe laser modulation amplitude should be on the order of the peak width in the

8 Page of AUTHOR SUBMITTED MANUSCRIPT - JPHYSB-.R modulation-free function T E ( c ) (i. e., within the lowest % in Figure. ). An application that stresses this point is discussed in next section.. Application of modulation spectroscopy to Rydberg-atom-based measurement of EM fields Rydberg atoms are large in size and electric-dipole transition moments, both scaling as n, and exhibit energy-level spacings in the microwave region, scaling as n. Rydberg atoms therefore respond sensitively to RF electric fields and are ideal candidates to measure such fields [,, ]. The RF field causes an AC Stark shift of the Rydberg level as well as modulation sidebands of the Rydberg level separated at even harmonics of the RF frequency. These features are employed in atom-based measurement of RF fields. S X,demod (arb.units) p0 / =. MHz p0 / =.0 MHz p0 / =. MHz p0 / =. MHz p0 / =. MHz ~ MHz Only RF field ~ -0MHz Only modulation (h) (g) (f) (e) (d) (c) (b) 0. EIT without modulation and RF field 0.0 (a) c X / (MHz) c R / (MHz) S R,demod (arb.units) Figure. (Color online) Measured EIT spectra for the X-output (left) and the R-output (right) of the lock-in amplifier. (a) Modulation-free EIT signal. (b) Demodulated EIT spectra of Rydberg atoms without applied RF field, with khz laser modulation frequency,. MHz laser modulation amplitude, and demodulation order q =. (c) Modulation-free EIT spectrum of Rydberg atoms in an RF field with frequency 0 MHz and amplitude. V/cm. (d-h) Demodulated RF EIT spectra, S X,demod ( c ) and S R,demod ( c ) with q =, for the indicated probe-laser modulation amplitudes. The RF field is same as for curve (c). Modulation spectroscopy can be used to improve the uncertainties in RFfrequency and field-amplitude measurements. To demonstrate this, we have applied the modulation method (laser modulation frequency khz) to analyze EIT spectra of

9 AUTHOR SUBMITTED MANUSCRIPT - JPHYSB-.R Page of Rydberg atoms subjected to an RF field of frequency 0 MHz and amplitude. V/cm. In Fig. curves (d-h) we show the demodulated spectra for q = in Eqs. and, for the indicated laser modulation amplitudes. The panels on the left show the X-output of the SR0 lock-in amplifier, corresponding to S X,demod ( c ) from Eq., while the ones on the right show the R-output, corresponding to S R,demod ( c ) from Eq.. For comparison, in Fig. we also show the modulation-free Rydberg-EIT signal in the absence of both RF field and laser modulation (curve (a)), the modulation-free Rydberg-EIT signal when the RF field is applied but the laser is not modulated (curve (c)), and the demodulated q = signal when the laser is modulated but the RF field is off (curve (b)). First, Fig. shows the anticipated RF-induced AC shift as well as even-harmonic sidebands of the Rydberg state [,, ]. It is evident from the curves (d-h) in Fig. that over the investigated range of the probe-laser modulation amplitude, p0, both the height and the signal-to-noise ratio of the demodulated signals, S X,demod and S R,demod, increase with p0. This is consistent with an elementary calculation based on Eqs. and, according to which the signal is proportional to p0 for modulation amplitudes p0 much less than the peak width of T ( c ), divided by ξ scale, and functions T ( c ) with peaks that are quadratic near the top. The increase in linewidth in the demodulated spectra is small, as expected from Figure (a). The spectra S X,demod ( c ) and S R,demod ( c ) in (b) and (d-h) have considerably better signal-to-noise ratio than the modulation-free EIT spectra in (a) and (c). This is largely due to the reduced linewidth of the central peaks seen in the demodulated spectra. We find linewidths of the central peaks in S X,demod and S R,demod that are two to three times smaller than those of the corresponding peaks in the modulation-free EIT signals. Data such as the ones presented in Fig. are valuable in a scenario in which the RF field is not a priori known. The RF sideband spectra in (c-h) then allow for an all-optical measurement of both the frequency and the electric-field amplitude of the applied RF field. The sideband separation ( MHz in Fig. ) reveals the RF frequency (which equals half the separation), whereas the measured AC shift of the main peak relative to the RF-free line and a polarizability calculation yield the RF field amplitude []. To extract the RF frequency, we obtain the autocorrelation functions of (c) and (h) and perform parabolic fits of the peaks at MHz, as shown in inset of Figure (a). The high signal-to-noise ratio of the auto- and cross-correlation functions in Fig. results from the fact that the correlations are obtained from integrals of the signal curves over much of the scan range in c. Hence, uncorrelated noise tends to integrate to zero. The fit results for the relevant peak centers in Fig. (a) are (. ± 0.00) MHz and (.0 ± 0.00) MHz, for the autocorrelation functions of (c) and (h), respectively. The RF frequency is given by half of that value [, ]. In our demonstration, wavelength modulation spectroscopy affords an uncertainty three times better than that obtained with modulation-free EIT spectra. Incidentally, the frequency measurement result deviates by about.% from the known value of the RF frequency. This appears to be due to a calibration uncertainty of the laser frequency c0. Therefore, since in the present case the RF frequency is known,

10 Page of AUTHOR SUBMITTED MANUSCRIPT - JPHYSB-.R Aotu-correlation (arb.units) (a) c&c c&c h&h h&h Frequency (MHz) Cross correlation function (arb. units) Frequency (MHz) Shift (MHz) (b) b&h a&c b&h Shift (MHz) a&c Figure. (Color online) (a) Auto-correlation function of curve (c) (red-solid line), and curve (h) (blue-dashed line) of the left panel of Figure. The inset shows a zoom-in over the frequency range of (-) MHz. (b) Cross-correlation functions of curves (a) and (c), and of curves (b) and (h) of the left panel of Figure. The RF-frequency and AC-shift values are obtained from parabolic fits of the peaks near MHz in (a) and near -0 MHz in (b) (fits shown as solid lines in the insets). the RF-modulation spectra allow for an improved re-calibration of the c0 -axis []. The cross correlation functions between (a) and (c), and between (b) and (h) in the left panel of Fig., yield respective readings for the RF-induced AC shift of (-.0 ± 0.00) MHz and (-. ± 0.00) MHz. Again, the measurement uncertainty for the AC shift achieved with wavelength modulation spectroscopy is better than that based on modulation-free EIT spectra. The deduced RF electric field experienced by the atoms, derived from the line shifts and a polarizability calculation, is. V/cm. This atomic measurement of the RF field is more accurate than the field value deduced from voltage readings and geometric / electric parameters of the system. In the latter, systematic uncertainties arise, for instance, from the RF transmission lines and amplifiers, and from the effects of the dielectric glass cell. In the present case, the electric-field value derived from the RF source voltage, geometric and electric parameters has an estimated uncertainty of %, whereas the atomic field measurement leads to an uncertainty in the sub-% range (dominated by systematic uncertainties). The presented example illustrates that the atomic measurement method bypasses

11 AUTHOR SUBMITTED MANUSCRIPT - JPHYSB-.R Page of conventional field calibration protocols and, instead, exploits the invariable nature of the atomic response to the RF field to obtain a better, atom-based field measurement. Figures and demonstrate that wavelength modulation spectroscopy yields improved spectroscopic signals that can further strengthen the atom-based field measurement method. We also note that the first-order output, q =, provides a dispersive curve that can be used to efficiently lock the coupling laser to the Rydberg transition (for details see [, ]).. Discussion We have studied the effect of probe-laser wavelength modulation on EIT spectra obtained with a cascade three-level system in a cesium room-temperature vapor cell. Demodulated signals at the first and second harmonic of the modulation frequency were measured versus the coupling-laser frequency. Over a wide range of the modulation amplitude we have explained the line shape and the peak separations in the demodulated spectra. Using small modulation amplitudes we have then shown that wavelength modulation spectroscopy applied in an EIT system enhances signal-to-noise ratio and sensitivity in weak-signal detection. Implementing modulation spectroscopy in an EIT setup for Rydberg-atom-based RF field measurement, we could improve uncertainties in RF frequency and AC Stark shift measurements by factors between two and three. Generally, the signal improvement afforded by wavelength modulation spectroscopy occurs because the method singles out the signal component at the modulation frequency (and at the proper phase). Noise at other frequencies is eliminated, including noise from electric power lines (0 Hz or 0 Hz) and interference from drivers for AOMs and EOMs (MHz to GHz range). In the present work modulation frequencies in the khz-range are employed because it is convenient to modulate laser diodes at such frequencies, and because transients of EIT signals are at much higher frequencies (in the MHz-range). We see no significant demodulated signals away from the EIT lines or when the modulation amplitude is set to zero. Therefore, there are no accidental acoustic or mechanical resonances near the modulation frequency (which could produce spurious signals). Wavelength modulation spectroscopy yields narrower spectral features at higher demodulation order (q in Eqs. and ). On the flip side, the amplitudes of demodulated signals drop at higher q, and the signal-to-noise ratio becomes worse. Therefore, as q is varied, there is a trade-off between linewidth and signal-to-noise. Here we have discussed the cases q = and. Depending on the details of a particular setup, the best trade-off between linewidth and signal-to-noise may occur at higher order (elsewhere we have seen best performance at q = ). We further anticipate improvements in the sensitivity of atom-based field measurement using a combination of Rydberg-EIT and wavelength modulation methods by reducing the peak width of the EIT response function, T E ( c ), in Eqs. and. This can be achieved by reducing the laser linewidth as well as the probe and coupling Rabi frequencies (at negligible laser linewidth, the width of the EIT window scales as

12 Page of AUTHOR SUBMITTED MANUSCRIPT - JPHYSB-.R (Ω c + Ω p)/γ), while increasing the atom-field interaction time by choosing larger beam diameters. Instead of wavelength-modulating the probe laser, one may modulate the Rydberglevel energy over a range on the order of MHz by applying an external EM field to the spectroscopic cell that has a frequency in the khz range. The demodulated EIT signals would follow equations similar to Eqs. and. Objectives of this extension of the work will include measurements of permanent electric and magnetic dipole moments as well as polarizabilities of atoms. Conversely, if the atomic response to the field is known, as is often the case, this atom modulation / signal demodulation method will enable the measurement of fields in the low-frequency (*LF) bands. Acknowledgements Funding. The work was supported by the Program (Grant No.CB0), Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (Grant No. IRT0), the State Key Program of National Natural Science of China (Grant No. 00), NNSF of China (Grants Nos., 00, and ), and Research Project Supported by Shanxi Scholarship Council of China (-00). GR acknowledges support by the NSF (PHY-0) and BAIREN plan of Shanxi province. References [] Harris S E Phys. Today 0 [] Holloway C, Gordon J, Jefferts S, Schwarzkopf A, Anderson D, Miller S, Thaicharoen N, and Raithel G, IEEE Transactions on Antennas and Propagation [] Bason M G, Tanasittikosol M, Sargsyan A, Mohapatra A K, Sarkisyan D, Potvliege R M, and Adams C S New J. Phys. 00 [] Jiao Y, Han X, Yang Z, Li J, Raithel G, Zhao J and Jia S, Phys. Rev. A 0 [] Miller S, Anderson D and Raithel G, New J. Phys. 00 [] Sedlacek J A, Schwettmann A, Kübler H, Löw R, Pfau T and Shaffer J P Nat. Phys., [] Fan H, Kumar S, Sedlacek H, Kübler H, Karimkashi S and Shaffer J P J. Phys. B 0 [] Sedlacek J A, Schwettmann A, Kübler H and Shaffer J P Phys. Rev. Lett. 000 [] Gordon J A, Holloway C L, Schwarzkopf A, Anderson D A, Miller S, Thaicharoen N, and Raithel G Appl. Phys. Lett. 0 [] Holloway C L, Gordon J A, Schwarzkopf A, Anderson D A, Miller S A, Thaicharoen N and Raithel G Appl. Phys. Lett. [] Hodgkinson J and Tatam R P Meas. Sci. Technol. 00 [] Xiao L, Li C, Li Q, Jia S and Zhou G 00 Appl. Opt. [] Xiao L, Zhao J, Yin W, Zhao Y, Jourent B and Jia S 0 Chin. Opt. Lett. [] Scully M O and Suhail Zubairy M Quantum optics (Cambridge University Press ) [] While the re-calibration would be straightforward, we have not performed it in order to point out another possible use of the RF modulation method. [] Jiao Y, Li J, Wang L, Zhang H, Zhang L, Zhao J and Jia S, Chin. Phys. B 0 [] Abel R P, Mohapatra A K, Bason M G, Pritchard J D, Weatherill K J, Raitzsch U, and Adams C S, 0 Appl. Phys. Lett. 0