Introduction

The generation of multi-photon states is highly desirable for quantum information processing applications such as photonic quantum computation and communication1. Quantum optical memories are likely to be critical components in such applications due to the probabilistic nature of photon sources and photonic gates2. Memories for classical and quantum light have been demonstrated in a plethora of systems, including cold atoms3,4,5, hot atomic vapor6,7,8, solid-state artificial atoms9,10,11, and all-optical storage loops12,13,14. With the exception of storage loops, these memories can offer continuous (on-demand) readout, required for synchronizing continuously pumped photon sources15,16,17.

Memories based on the spin coherence of atomic ensembles, where both the signal photon and classical control field couple to the ground electronic orbital, have been extensively studied due to their potential for high storage efficiency18,19,20,21 and long storage time22,23,24,25. However, it is difficult to obtain noise-free operation in these memories due to four-wave mixing (FWM) noise26 and, in memories based on warm atomic ensembles, spontaneous Raman scattering from imperfect optical pumping21. These issues become even more pronounced, and eventually detrimental, when operating at warm temperatures and at high bandwidths that are comparable to the hyperfine splitting. Additionally, low-noise operation requires filtering out the strong control field, which typically requires etalon filters that reduce the signal transmission and hence the memory’s end-to-end efficiency18,19,20,21.

An alternative to the spin memory is the orbital memory27,28,29, where the excitation scheme is of a ladder-type, and the light is stored on a doubly-excited orbital. Although the memory lifetime is inherently limited by the lifetime of the orbital level, orbital memories are immune to FWM noise due to the ladder excitation scheme and the wavelength mismatch between the signal and control transitions27,28. Since the storage level is not populated even at high temperatures, the spontaneous Raman scattering noise is eliminated. Furthermore, the wavelength mismatch also enables the filtering of the strong control field from the retrieved signal field using conventional thin-film interference filters (IFs) with high transmission.

A fast ladder memory (FLAME) based on off-resonant cascaded absorption was demonstrated in cesium vapor by Kaczmarek et al.28 and rubidium vapor by Thomas et al.29. In these demonstrations, the large wavelength mismatch between the signal and control fields resulted in a substantial residual Doppler broadening that limits the memory lifetime to a few ns. A much smaller mismatch exists for the ladder scheme \(\vert 5{S}_{1/2}\rangle \to \vert 5{P}_{3/2}\rangle \to \vert 5{D}_{5/2}\rangle\) in rubidium, for which the signal and control wavelengths are 780 and 776 nm, respectively. As demonstrated by Finkelstein et al.27, the reduced residual Doppler broadening of this cascaded transition enables a memory lifetime of ~130 ns in the absence of other decoherence mechanisms.

Here we report on an upgraded FLAME setup (FLAME-2) which has several improvements over the original demonstration (FLAME-1)27. FLAME-2 uses an auxiliary, off-resonant dressing field that counteracts the residual Doppler broadening and further increases the memory lifetime30. To increase the memory efficiency and reduce the noise, FLAME-2 employs a longer vapor cell, which provides higher optical depth (OD) at a lower atomic density, and an annular optical pumping beam. Finally, the control field of FLAME-2 is stronger, which increases the memory efficiency for the on-resonance storage scheme, and the signal beam diameter is larger, reducing time-of-flight decoherence. As part of the characterization of FLAME-2, we study on-resonance storage (also known as electromagnetically-induced-transparency storage31) and off-resonance storage (pertaining to Raman storage32) of nanosecond-long pulses with variable width.

Results

Experimental scheme

We use the stretched states of the 87Rb level system shown in Fig. 1a. The signal pulse with a wavelength of 780 nm couples the \(\vert 5{S}_{1/2},F=2,{m}_{F}=2\rangle \to \vert 5{P}_{3/2},F=3,{m}_{F}=3\rangle\) transition with a detuning Δ = 0 (Δ = 1.1 GHz) for on-resonance (off-resonance) storage. The control field with a wavelength of 776 nm is detuned from the \(\vert 5{P}_{3/2},F=3,{m}_{F}=3\rangle \to \vert 5{D}_{5/2},F=4,{m}_{F}=4\rangle\) transition such that the two-photon transition \(\vert 5{S}_{1/2}\rangle \to \vert 5{P}_{3/2}\rangle \to \vert 5{D}_{5/2}\rangle\) is almost on-resonance. The auxiliary dressing field with a wavelength of 1274 nm is detuned by Δd = − 570 MHz from the \(\vert 5{D}_{5/2}\rangle \to \vert 28{F}_{7/2}\rangle\) transition. Lastly, the pump and repump fields, used to optically pump the atoms to the maximal spin state \(\vert 5{S}_{1/2},F=2,{m}_{F}=2\rangle\), have a wavelength of 795 nm and couple the \(\vert 5{S}_{1/2},F=2\rangle \to \vert 5{P}_{1/2},F=2\rangle\) and \(\vert 5{S}_{1/2},F=1\rangle \to \vert 5{P}_{1/2},F=2\rangle\) transitions, respectively (not shown in Fig. 1a). Experimental details on the generation of the light fields used in the experiment are given in the methods section.

Fig. 1: FLAME-2 system.
figure 1

a The ladder-level scheme of 87Rb. Initially, the atoms are optically pumped to the \(\vert 5{S}_{1/2},F=2,{m}_{F}=2\rangle\) ground state, where F is the total angular momentum of the valence electron and mF is the angular momentum projection on the optical axis. The memory operates with all-orbital transitions to generate coherence between the ground state and the doubly-excited state \(\vert 5{D}_{5/2},F=4,{m}_{F}=4\rangle\). The latter is off-resonantly coupled to the auxiliary state \(\vert 28{F}_{7/2}\rangle\) in order to compensate for the residual Doppler broadening of the \(\vert 5{S}_{1/2}\rangle \to \vert 5{P}_{3/2}\rangle \to \vert 5{D}_{5/2}\rangle\) transition. b The experimental setup. The signal and control beams counter-propagate inside the vapor cell. The pump and repump beams are reflected from a spatial light modulator (SLM) to generate an annular beam inside the vapor cell and are inserted with a slight angle to the optical axis. The dressing beam is combined with the signal beam on a dichroic mirror. c Characteristic measurement with and without the memory operation. Shown are the reference signal pulse (blue), the stored and retrieved pulse for on-resonance storage (orange), and the control pulses (dashed-dotted gray). The shaded areas indicate the integration window size used for calculating memory efficiency. DM dichroic mirror, FC fiber coupler, FLAME fast ladder memory, HWP half-wave plate, IF interference filter, M mirror, PBS polarizing beam splitter, QWP quarter-wave plate, SMF polarization-maintaining single-mode fiber, SPCM single-photon counting module.

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Figure 1b shows the experimental setup. All fields are σ+ polarized inside the medium. The signal field counter-propagates with the control field inside a 25-mm-long isotopically purified 87Rb vapor cell. The cell is placed inside three layers of mu-metal magnetic shielding and heated to ~65 ∘C. The dressing field co-propagates with the signal field.

The counter-propagating signal and control fields render the residual Doppler broadening of the two-photon transition very small. Nevertheless, to further suppress the residual Doppler broadening caused by their small wavelength difference, we employ a “continuous protection” scheme previously developed in our lab30. Here, the velocity-dependent Doppler shift is continuously compensated by a velocity-dependent light shift, induced by the auxiliary dressing field (see Methods).

The pump and repump fields are reflected from a spatial light modulator (SLM) to generate an annular beam that does not overlap the signal inside the vapor cell. During the pumping, part of the atomic population is excited to the 5P1/2 level. These atoms can collide and transfer the population to the 5D5/2 level via an energy-pulling process33. This incoherent population can then decay to the 5P3/2 state, from which it fluoresces and adds noise to the signal channel27. The annular beam spatially separates the pump beams from the signal, and thus reduces the noise in the output mode. The optical pumping efficiency of the F = 2 ground level to the maximal spin state (mF = 2) is 94 ± 2%. Errors of system characterization represent 1 standard deviation (s.d.) of measurement uncertainty.

The output signal is sent to a single-photon counting module through a single-mode, polarization-maintaining fiber. There is no need to use etalon filters to clean the signal, due to the wavelength difference between the signal and control fields. Instead, we use two narrow-band IFs with 3-nm full-width at half-maximum (FWHM) in the output signal channel to filter out the residual control, pump, and repump fields, and a short-pass IF to filter out the residual dressing field. Additionally, we have one IF in the input signal channel, which prevents residual control light from coupling into the signal input fiber; This light might undergo spontaneous Raman scattering inside the fiber34, which is frequency shifted and, therefore, partially transmitted through the IF of the output signal. Lastly, we use a dichroic mirror in the pump-repump input channel to block residual 780-nm light. The transmission of the signal field through the memory setup, from immediately after the input signal beam fiber and into and out of the output fiber, is 66 ± 2%. It is comprised of transmission through the vapor cell (88 ± 1%), transmission through the optical filters (94 ± 1%), coupling to the output fiber (88 ± 2%), and the transmission of all other optical elements (91 ± 2%). In the off-resonance storage, the transmission through the vapor cell is reduced to 75 ± 2% due to absorption by residual 85Rb.

Figure 1c shows a typical measurement of the memory experiment. Initially, we measure the signal pulse (count histogram shown in blue) when it is far-detuned from the atomic absorption line. Next, we turn on the control pulses (dashed-dotted gray) and again measure the signal output (orange; here, shown for on-resonance storage). The first control pulse generates a coherent absorption of the signal field and maps it into the coherence between the ground and doubly-excited state, which is retrieved with the application of the second control pulse. Throughout the paper, unless specified otherwise, the signal pulse is a Gaussian pulse with an FWHM of 2 ns. The shaded areas in Fig. 1c (light blue and light orange) are the integration windows (6-ns long) used to calculate the total photon number in the reference and retrieved pulses from which we calculate the memory efficiency. For the noise measurements, we block the signal input and integrate the photon counts in the same time window as for the retrieved pulse.

Memory characterization

We begin the memory characterization by optimizing the length of the control pulse, the two-photon detuning, and the OD to achieve maximal storage and retrieval efficiency. We find the optimal control FWHM to be 4 ns (3 ns) for on-resonance (off-resonance) storage. We note that further increasing the control pulse length reduces the memory efficiency, which might not be expected for on-resonance storage. We attribute this to a reduction in the control pulse amplitude for longer pulses in our system. The optimal two-photon detuning is found at slightly negative values of −50 MHz (−20 MHz), providing a relative efficiency increase of 2 ± 1% (1 ± 1%) for on-resonance (off-resonance) storage. In the off-resonance storage, this nonzero optimal detuning is due to control-induced light-shifts. In the on-resonance storage, it is due to the residual absorption of un-pumped atoms to the Doppler-broadened \(\vert 5{P}_{3/2},F=1,2\rangle\) states. We set the vapor temperature such that the OD, measured on the \(\vert 5{S}_{1/2},F=2\rangle \to \vert 5{P}_{3/2},F=3\rangle\) transition, is OD = 19 ± 1. Further increasing the OD saturates the storage efficiency while increasing the noise induced by the optical pumping beams.

Figure 2 shows the memory efficiency versus storage time t with and without the dressing field for on-resonance and off-resonance storage. We find that the memory efficiency is higher for on-resonance storage when there is sufficient control power. This is to be expected, primarily as our control pulses are not chirped, as required for optimal off-resonance storage35.

Fig. 2: Memory efficiency.
figure 2

a, b Efficiency (storage and retrieval) versus the storage time for (a) on-resonance and (b) off-resonance storage, without the dressing field (blue) and with the dressing field (red). The left axis is the internal memory efficiency (ηint), and the right axis is the memory end-to-end efficiency (ηe2e) that includes the signal transmission through the entire memory setup. Circles are the measured data; the standard deviation of the mean of repeated measurements is smaller than the circles' size. The lines are fits to a model comprising exponential and Gaussian decays. The black arrows in (a) show the zero-time efficiency. For comparison, we show in gray the internal efficiency of FLAME-127 (see Memory characterization section for details).

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Adding the dressing field imparts a velocity-dependent light shift which counteracts the motional decoherence due to the residual Doppler broadening of the \(\vert 5{S}_{1/2}\rangle \to \vert 5{P}_{3/2}\rangle \to \vert 5{D}_{5/2}\rangle\) transition30. The dressing is kept constantly on, and we observe almost no decrease in memory short-time efficiency. The benefit of the dressing field is most significant at long storage times (t > 80 ns), where it increases the memory efficiency by >10%.

We model the memory efficiency versus time as \(\eta (t)=\eta (0){e}^{-{t}^{2}/2{\tau }_{\sigma }^{2}-t/{\tau }_{\gamma }}\), with Gaussian (τσ) and exponential (τγ) decoherence times. The Gaussian term originates from the residual Doppler broadening and the Maxwell-Boltzmann velocity distribution, whereas the exponential term originates mainly from the finite lifetime of the 5D5/2 level and the time-of-flight broadening through the beam36. We extract the memory 1/e lifetime τs from η(τs) = η(0)e−1 (see Finkelstein et al.27 for details). Using the dressing field increases the 1/e lifetime from τs = 90 ± 3 ns (102 ± 2 ns) to τs = 108 ± 2 ns (113 ± 2 ns) for on-resonance (off-resonance) storage, while keeping the zero-time efficiency η(0) almost unchanged. With the dressing field, we measure an internal (end-to-end) short-time memory efficiency of ηint(0) = 52.6 ± 0.8% [ηe2e(0) = 34.7 ± 1.2%] for the on-resonance storage, and ηint(0) = 39.8 ± 0.6% [ηe2e(0) = 22.3 ± 0.9%] for the off-resonance storage. Here the errors are 1 s.d. of the fit uncertainty.

For the sake of comparison, Fig. 2 also shows ηint(t) of the original FLAME-1. The most significant increase in memory efficiency is observed for on-resonance storage. The temporal oscillations, which arise in FLAME-1 from destructive interference between 5D5/2 hyperfine states due to imperfect optical pumping27, are nearly eliminated in FLAME-2. Note that ηe2e(t) of FLAME-1 is higher than shown in Fig. 2 by 18% (39%) for on- (off-) resonance storage, mainly due to better transmission of the glass cell windows (and, in the off-resonance case, lower residual 85Rb absorption due to different signal detuning). The end-to-end efficiency of FLAME-2 and FLAME-1 is compared in Table 1.

Table 1 Comparison of this work (FLAME-2) and the original demonstration (FLAME-1)27.
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The dependence of the memory efficiency on the peak power of the control field is shown in Fig. 3a for a storage time of 20 ns. For each control power, we optimize the control pulse timing and find that higher control powers require earlier timing to maximize the efficiency. On-resonance storage reaches higher efficiencies but necessitates a stronger control field, as it requires generating a deep-enough transparency window within the Doppler-broadened absorption line.

Fig. 3: Dependence of efficiency and noise on the control power.
figure 3

a The memory efficiency at a storage time of 20 ns. Note that here and in Fig. 4, the ηe2e axis refers to the end-to-end efficiency of the on-resonance storage; the off-resonance storage efficiency is 15% lower due to absorption by residual 85Rb atoms. b The mean number of noise photons per retrieved pulse. The lines are a linear fit. Results are shown for (green) on-resonance storage and (orange) off-resonance, both with the dressing field. In (a, b) the error bars are the standard deviation of the mean of repeated measurements.

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Figure 3b shows the mean number of added noise photons from memory versus the control power. The noise per pulse caused by the pump beams is νp = (0.92 ± 0.07) × 10−5 photons. The noise originating from the control field increases linearly to a level of νc(Pc = 1 W) = (1.67 ± 0.16) × 10−5 photons for on-resonance storage and νc(Pc = 1 W) = (1.46 ± 0.14) × 10−5 photons for off-resonance storage, where Pc is the control power. This residual noise originates from reflection and perhaps a nonlinear frequency shift of the control field at the vapor cell facets. The dressing field does not add noise within the measurement uncertainty.

We study the memory bandwidth in Fig. 4. Here, for each signal pulse length, the control power and timing are optimized. For all measured signal pulses, the on-resonance storage has a higher efficiency than the off-resonance storage. As expected, the highest efficiency is obtained for the longer (>1.5 ns) signal pulses. While the efficiency reduces for shorter pulses, the effective fractional delay, which determines the potential enhancement of multi-photon rates in a synchronization application2, is actually increased when shortening the signal photons.

Fig. 4: Memory bandwidth.
figure 4

The memory efficiency versus the signal pulse length is measured for a storage time of 20 ns with the dressing field. The efficiency is maximal for a 2-ns-long signal. Vertical error bars are the standard deviation of the mean of repeated measurements, and horizontal error bars are 1 standard deviation of the fit uncertainty.

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Discussion

Table 1 compares the performance of the upgraded memory FLAME-2 to the original FLAME-127. In FLAME-1, the off-resonance storage was slightly more efficient than the on-resonance storage, whereas in FLAME-2, the on-resonance storage is more efficient. This expected result is mainly due to the higher available control power. The efficiency is further improved in FLAME-2 by using a higher OD. In the off-resonance storage, the end-to-end efficiency of FLAME-2 is slightly lower than that of FLAME-1 due to a lower transmission through the vapor cell, caused mainly due to a different signal field detuning, which is on-resonance with the residual 85Rb. The mean number of added noise photons ν in FLAME-2 is lower than in FLAME-1 due to the reduced atomic density in the longer vapor cell and the annular optical pumping beams. Therefore, the noise-to-signal ratio for one input photon, μ1 = ν/ηe2e(0), is also lower. The lifetime of FLAME-2 is increased by working with a larger signal beam that reduces the time-of-flight broadening and by employing the dressing field to counteract the residual Doppler broadening of the two-photon transition. Overall, FLAME-2 improves on FLAME-1 in all parameters.

The end-to-end memory efficiency, storage time, and acceptance bandwidth are the key ingredients for enhancing photon synchronization rates. In our setup, the memory internal efficiency for on-resonance storage is limited firstly by the finite width of the control beam37, which is only ~60% wider than the signal beam, and by the imperfect optical pumping that causes residual absorption to the \(\vert 5{P}_{3/2},F=1,2\rangle\) states. By improving the optical pumping and increasing the control beam waist (while keeping the peak intensity the same), we estimate that an internal efficiency above 70% is readily achievable for on-resonance storage. Further improving the memory internal efficiency will require replacing the Pockels cells that generate the control pulses in order to eliminate the after-pulse and optimize the control shape to the input signal pulse35,38. This can be achieved by using an amplitude electro-optics modulator (EOM) that seeds a tapered amplifier (TA)8.

The acceptance bandwidth of the memory is limited by the bandwidth of our control pulses. Using an amplitude EOM to generate the control pulses will thus enable, in principle, the storage of shorter signal photons. However, this will also necessitate higher control powers, which are currently unavailable with tapered amplifiers. Finally, the end-to-end efficiency can be improved by increasing the setup transmission using a vapor cell with higher transmission and an output optical fiber with an anti-reflection coating. Realistically these can increase the overall transmission by about 10%.

In conclusion, we demonstrate an upgraded FLAME with high end-to-end efficiency, high bandwidth, and low noise. It outperforms the original FLAME demonstration in all of these parameters, and we outline a path for further improvements. The upgraded memory can be readily used to synchronize single photons with compatible wavelength and bandwidth, such as those generated in spontaneous cascaded emission15,16.

Methods

Experimental details

The signal field originates from a continuous-wave (CW) distributed Bragg reflector (DBR) laser, which is offset-locked to a stable master laser, and passes through two amplitude EOMs to generate the signal pulses. We use an arbitrary waveform generator (PicoQuant PPG512) to generate Gaussian-like pulses with variable widths and stabilize the bias of the EOMs to achieve a pulse extinction ratio (ER) of >1:10,000. We attenuate the signal pulse intensity to an average of ~0.1 photons per pulse.

The control field originates from a CW Ti:Sapphire laser. The storage and retrieval control pulses are generated with two free-space Pockels cells between cross-polarizers with a pulse ER of >1:800 and peak power at the vapor cell of 1.4 W. The 10−90% rise and fall time of the pulses are ~1.2 ns, and the width of the pulses is variable. The timing of the signal and control pulses is controlled by a digital delay generator with a 10 ps timing resolution which operates the experimental sequence at a repetition rate of 105 cycles per second.

The auxiliary dressing field originates from an external cavity diode laser. It is initially amplified by an O-Band booster optical amplifier and further amplified by a TA. The dressing power at the vapor cell is set to 135 mW. The pump and repump fields originate from DBR lasers amplified by TAs and have a power of 370 mW (105 mW) for the pump (repump) before the vapor cell. The pump (repump) detuning is −200 MHz (+150 MHz). The frequencies of the control and dressing (pump and repump) lasers are stabilized using a wavelength meter with a resolution of 1 MHz (10 MHz).

The signal field is focused to a 1/e2 waist radius of w0 = 110 μm inside the vapor cell. The control field has a waist radius of w0 = 180 μm, and the dressing field has a waist radius of w0 = 210 μm. The Rabi frequencies of the control and dressing fields (corresponding to 1.4 W and 135 mW) are Ωc = 640 ± 50 MHz and Ωd = 30 ± 5 MHz, respectively. The pump and repump annular beam is generated by imprinting an L = 4 Laguerre-Gauss phase-mask on the SLM, and has internal (external) diameters of 400 μm (1 mm) inside the vapor cell. This beam is inserted into the vapor cell with a D-shaped mirror at an angle of ~0.85∘ to the optical axis, counter-propagating with respect to the signal field.

Compensating the residual Doppler broadening

For a single excitation, the collective state of the atoms immediately after the first control pulse is30,39

$$\left\vert W(0)\right\rangle =\frac{1}{\sqrt{N}}\mathop{\sum}\limits_{j}{e}^{-i\Delta k{z}_{j}}{\left\vert \uparrow \right\rangle }_{j}\langle \downarrow {| }_{j}| G\rangle ,$$
(1)

where Δk = ks − kc is the wavevector mismatch of the two-photon transition, zj is the position of the jth atom, and \(\left\vert G\right\rangle ={\prod }_{j}{\left\vert \downarrow \right\rangle }_{j}\) is the collective ground state. Due to the ballistic thermal motion, after a time t the atoms carry the original phase to position zj + vjt and the collective atomic state reads

$$\left\vert W(t)\right\rangle =\frac{1}{\sqrt{N}}\mathop{\sum}\limits_{j}{e}^{-i\Delta k({z}_{j}+{v}_{j}t)}{\left\vert \uparrow \right\rangle }_{j}\langle \downarrow {| }_{j}| G\rangle .$$
(2)

Neglecting the spontaneous decay of the excited state atoms and the time-of-flight broadening of the atoms moving transversely out of the beam, the storage efficiency versus time is given by ηint(t) = ηint(0)∣〈W(0)∣W(t)〉∣2 30,39. Thus, the residual Doppler broadening Δk ≠ 0 induces a decay of the retrieval efficiency.

Adding a far-detuned dressing beam, atom j experiences a light shift of approximately \(-{\Omega }_{{{{{{{{\rm{d}}}}}}}}}^{2}/({\Delta }_{{{{{{{{\rm{d}}}}}}}}}-{k}_{{{{{{{{\rm{d}}}}}}}}}{v}_{j})\), for kd ≫ Δk. Expanding to the first order in kdvj/Δd, the accumulated phase each atom acquires due to the dressing field is

$${\phi }_{{{{{{{{\rm{d}}}}}}}}j}(t)\approx -\left[\frac{{\Omega }_{{{{{{{{\rm{d}}}}}}}}}^{2}}{{\Delta }_{{{{{{{{\rm{d}}}}}}}}}}+\frac{{\Omega }_{{{{{{{{\rm{d}}}}}}}}}^{2}}{{\Delta }_{{{{{{{{\rm{d}}}}}}}}}^{2}}{k}_{{{{{{{{\rm{d}}}}}}}}}{v}_{j}\right]t.$$
(3)

The first term is a global phase shift, whereas the second term is a velocity-dependent phase shift.

In order to compensate for the residual Doppler broadening, we require that \(({\Omega }_{{{{{{{{\rm{d}}}}}}}}}^{2}/{\Delta }_{{{{{{{{\rm{d}}}}}}}}}^{2}){k}_{{{{{{{{\rm{d}}}}}}}}}{v}_{j}+\Delta k{v}_{j}=0\) for all j. This is achieved for the ‘compensation condition’

$$\frac{{\Omega }_{{{{{{{{\rm{d}}}}}}}}}^{2}}{{\Delta }_{{{{{{{{\rm{d}}}}}}}}}^{2}}\approx \frac{-\Delta k}{{k}_{{{{{{{{\rm{d}}}}}}}}}}.$$
(4)

When this condition is met, to first order in the velocity, the atoms do not experience a velocity-dependent phase. In our experiment, the second-order terms in the velocity and the finite size of the dressing Gaussian beam limit the prefect cancellation of the residual Doppler broadening. In the ladder-level system we employ, ∣Δk∣/kd ≈ 1/110. This means that at the compensation condition the population in the 28F state is negligibly small, and therefore the short-time memory efficiency almost does not deteriorate due to the dressing field.