Toward a Scalable Linear-Cavity Enhanced Warm-Vapor Photonic Quantum Memory

Abstract

The coherent storage, buffering and retrieval of photons in a quantum memory enables the scalable creation of photonic entangled states via linear optics and repeat-until-success, unlocking applications in quantum communications and photonic quantum computing. Quantum memories based on off-resonant cascaded absorption (ORCA) in atomic vapors allow this storage to be broadband, noise-free, and high efficiency. Here, we implement a cavity-enhanced ORCA memory with reduced footprint and reduced power requirements compared to conventional single-pass schemes. By combining a strong magnetic field with polarization control, we maintain a Doppler-free interaction and eliminate the need for optical pumping. Our design establishes the feasibility of large arrays of ultra-compact, low-power, near-unit-efficiency, noiseless quantum memories running at GHz bandwidth, without the need for atom trapping or cryogenics.

Figures (5)

• Figure 1: (a) Schematic of the experimental setup indicating the key components. AL: Aspheric fibre collimation lens of focal length 4.5mm; SL: Plano-convex singlet lens of focal length 100 mm used for mode-matching the signal and control beams to the TEM$_{00}$ mode of the cavity; PBS: Plate polarization beam splitter used to combine the signal and the control beams; M$_{1}$: Cavity in-coupling mirror with anti-reflection coating on the planar side and high reflection coating on the concave side with a reflectivity of 60%; M$_{2}$: Cavity end mirror with a reflectivity 99.98% for the concave side; QWP: Quarter wave plates used to rotate the polarization by 90 degrees upon each reflection in the cavity; VC: Vapour cell containing isotopically pure $^{87}$Rb; PM: Ring shaped permanent magnets used to produce axial magnetic field along the propagation direction $z$. The input signal and control couples in to the cavity via the mirror M$_{1}$. The signal output couples through the same optical fibre. An optical circulator is used to separate the output signal from the input and sent to the SNSPD for detection. Polarization of the intra-cavity fields are circular and correlated to their propagation directions. Field Polarization driving $\sigma-$ transitions in the atoms are indicated using solid lines and that driving $\sigma+$ transitions are indicated with dashed lines. (b) Simplified level scheme. Transition frequencies for dipole allowed transitions with polarisation combination other than ($\sigma-$, $\sigma-$) for signal and control fields are shifted off-resonance by the strong B-field as indicated in the level scheme. (c) The 2D plot shows modelling of the signal-control resonances for the design parameters used in our experiment; The signal and control frequencies are expressed in terms of detunings $\Delta$ and $\delta$ from the respective atomic transitions. The darker (red-orange) circular spots indicate the signal-control frequency pair for which the dual resonance criteria is satisfied. The black dashed line indicates the parametric line that satisfies the two-photon resonance i.e.,$\delta$ = $-\Delta$. The arrow labelled L indicates the direction in which the resonances shift when the mirror spacing is changed by temperature tuning. We measure a resonance shift of $\approx$ 3.2 GHz/$^\circ$C.
• Figure 2: The detection of signal pulses on the SNSPD is shown in plot (a), and the corresponding control pulse detection using a fast photodiode and an oscilloscope is shown in plot (b). In the signal mode, a reference pulse followed by an identical storage pulse is sent to the memory. A write control pulse overlapping in time with the storage pulse results in absorption of the signal into the memory. The unstored signal is detected as leak pulse by the SNSPD. After a storage time of 12.5 ns a read control pulse is sent to the memory which retrieves the stored signal and is detected as retrieved pulse by the SNSPD. The ratio of total counts in the retrieved pulse to the reference pulse ($C_{ret}/C_{ref}$) is proportional to the memory efficiency, and is used as a objective function for maximising the efficiency. The results of a real-time optimisation run is shown in the plots (c) to (j). It can be seen that value of the objective function in (c) initially grows with iteration number as the various experimental parameters steer towards their optimal values, but the cavity resonance drift prevents convergence. The features in the measurement corresponding to some of these parameters are annotated in the plots (a) and (b). The pulse widths in (g), (h) and (j) are defined at full-width-half-maximum. The two-photon detuning in (d) is tuned using control detuning $\delta$. At the start of the optimisation, we tune the control laser frequency to hit the two-photon resonance i.e.,$\delta$ = $-\Delta$. (k) Noise counts in the signal mode for the same integration time used in (a). The plot shown is obtained from average of counts measured for 1000 traces.
• Figure 3: (a) Memory efficiency measured as a function of signal storage time. The black (dashed) line shows the fit to the model described in the text. (b) Memory efficiency at 12.5 ns storage time as a function of control pulse energy of the write pulse. The fraction of the read pulse energy to write pulse energy and the other parameters are fixed at the optimum value. The pulse energy is determined from the detection of control pulse amplitude using a fast photodetector. The error in pulse energy comes from the uncertainty in photodetector sensitivity and losses. (c) Memory efficiency vs signal pulse temporal width expressed in Gaussian Full-Width-at-Half-Maximum (FWHM).
• Figure 4: (a) Setup used to characterise the cavity performance. The cavity response is measured using a signal and/or control laser in cw operation in reflection and transmission using photodetectors PD1 and PD2 respectively. (b) Frequency response of the cavity in reflection measured using a weak cw signal laser shown in blue. The 776 nm control laser is switched off for this measurement. The frequency is expressed in terms of detuning ($\Delta$) from $5S_{1/2} \rightarrow 5P_{3/2}$ central frequency shown in Figure \ref{['fig:spectroscopy']}(b). Curve fit to the model described in the text is shown as black dashed line with the shaded grey areas showing the uncertainty due to parameter errors. (c) Frequency response with a weak signal laser and a strong control laser. Signal frequency is tuned to be on-resonance with the cavity and an atomic intermediate state detuning of $\approx\,-11$ GHz in (b). The control frequency is scanned and its transmission through the cavity measured on PD2 shown as red line in the plot. The signal detection on PD1 shown as blue line reveals two narrow two-photon absorption lines occurring within the cavity bandwidth with a frequency separation of $\approx$175 MHz.(d) Zoomed in to show the shaded region in (c) i.e., the stronger of the two absorption lines. The black dashed line is a fit to Gaussian broadened absorption line used to determine the FWHM width of 11.8$\pm$2.4 MHz.
• Figure 5: (a) Breit-Rabi diagram with the states labelled from 1 to 48. The grey shaded region indicates the level spacings for the magnetic field used in the experiment. The relevant transitions at this magnetic field is shown on the right with the three-levels used for the memory is highlighted in cyan. The state vectors indicate the total spin and nuclear spin quantum numbers $m_j$ and $m_i$ of the states along the direction of the B-field. (b) Experimental setup used to perform spectroscopy. A weak 780 nm cw signal beam used as a probe passes through the vapour cell, and its transmission is detected using a photodetector (PD) and an oscilloscope. A strong cw control beam at 776 nm is used for two-photon spectroscopy. It is aligned to overlap with the signal in the vapour cell. A permanent magnet PM is used to produce the B-field. Both the control and the signal fields are produced by Toptica DLPro external cavity diode lasers (ECDL). (c) One-photon absorption spectroscopy performed using $\sigma-$ signal beam. The control beam is blocked for this measurement. The frequency of the signal is expressed in terms of detuning from the $5S_{1/2} \rightarrow 5P_{3/2}$ central frequency shown in (a). The measured absorption dip is shown as coloured (blue) line. Model fit to theory indicated in black solid line is used to determine the B-field strength to be $169\pm3$ mTesla. The only other fit parameters include frequency offset, and atomic vapour optical depth. The Doppler broadening width and the relative transition strengths of the lines are fixed according to the theory. The deviation of the measured dip from the theory is mainly due to non-linear response of the piezo voltage scan used for frequency tuning the laser, which leads to systematic error in the attributed frequency of the probe beam. (d) Two photon absorption spectrum of the signal beam measured by scanning the frequency of the control laser. The frequency of the signal is fixed to a frequency corresponding to 0 GHz in (c). The polarizations of both signal and control were set to $\sigma-$ for this measurement. The vertical dotted lines indicate strong absorption lines from theory. The blue lines indicate transitions with $\sigma-$ polarization for both signal and control fields which is the configuration used for memory. The grey lines indicate the transitions for other pairs of polarization that would result in signal loss in the cavity. Refer to supplementary material for the relative transition strengths and detunings suppl.