Simple atomic quantum memory suitable for semiconductor quantum dot single photons

TL;DR

This paper demonstrates a warm vapor quantum memory compatible with semiconductor quantum dot single photons, achieving on-demand storage with promising efficiency and low noise, suitable for future quantum networks.

Contribution

It introduces a simple atomic quantum memory in warm Rb vapor optimized for semiconductor quantum dot photons, with measurable efficiency and low noise, advancing practical quantum memory development.

Findings

End-to-end efficiency of 3.4% at 50 ns storage time

Intrinsic efficiency of 17%, with potential to reach 35%

Memory bandwidth of 0.66 GHz suitable for quantum dot photons

Abstract

Quantum memories matched to single photon sources will form an important cornerstone of future quantum network technology. We demonstrate such a memory in warm Rb vapor with on-demand storage and retrieval, based on electromagnetically induced transparency. With an acceptance bandwidth of $\delta f$ = 0.66~GHz the memory is suitable for single photons emitted by semiconductor quantum dots. In this regime, vapor cell memories offer an excellent compromise between storage efficiency, storage time, noise level, and experimental complexity, and atomic collisions have negligible influence on the optical coherences. Operation of the memory is demonstrated using attenuated laser pulses on the single photon level. For 50 ns storage time we measure $\eta_{\textrm{e2e}}^{\textrm{50ns}} = 3.4(3)\%$ \emph{end-to-end efficiency} of the fiber-coupled memory, with an \emph{total intrinsic efficiency} $\eta_{\textrm{int}} = 17(3)\%$. Straightforward technological improvements can boost the end-to-end-efficiency to $\eta_{\textrm{e2e}} \approx 35\%$; beyond that increasing the optical depth and exploiting the Zeeman substructure of the atoms will allow such a memory to approach near unity efficiency. In the present memory, the unconditional readout noise level of $9\cdot 10^{-3}$ photons is dominated by atomic fluorescence, and for input pulses containing on average $\mu_{1}=0.27(4)$ photons the signal to noise level would be unity.

Full text

††preprint: APS/123-QED

Quantum networks built from optical fiber-linked quantum nodes Kimble2008 open manifold opportunities across a range of scientific and technological frontiers. For example: high-speed quantum cryptography networks can be used for unconditionally secure communication in metropolitan areas Gisin2002 ; and quantum networks can help realize large scale quantum computers and quantum simulators that will allow for exponential speed-up in solving complex problems Ladd2010 ; Kok2007 . Photonic quantum networks, in turn, require a scalable quantum node technology that allows for (i) storing quantum information in a quantum memory Bussieres2013 ; and (ii) on-demand conversion of this information into single photons traveling along the network interconnects.

To realize quantum nodes, a heterogeneous approach Sangouard2007 ; Sangouard2011 is highly promising. Heterogeneous quantum nodes consist of a single photon source and a compatible quantum memory, where the systems may be completely different from each other and can be individually optimized. For the single photon source, self-assembled semiconductor quantum dots (QD) are arguably the best choice, as they allow for high speed on-demand photon generation with up to GHz emission rates and measured efficiencies Munsch2013 ; Somaschi2015 ; Ding2016 as high as 75%. These sources can emit indistinguishable single photons Somaschi2015 ; Santori2002 ; Ates2009 , or even polarization-entangled photon pairs Stevenson2006 ; Chen2016 , and the QD spin can be entangled with an emitted photon Delteil2016 ; Gao2012 . However, the quantum dot itself is not a good quantum memory, since the coherence times are limited by the comparably strong coupling to the solid-state environment. To make this exquisite source of single or entangled photons useful for quantum networks, the QD therefore has to be combined with a quantum memory with a high end-to-end efficiency. In this letter, we present such a memory based on warm rubidium vapor. The developed memory can readily be combined with a well-engineered GaAs/AlGaAs QD single photon source Jahn2015 ; Munsch2013 ; Akopian and may then serve as a network node, bringing the vision of functional quantum networks closer to reality.

Many different physical platforms for quantum memories are currently unter investigation, ranging from phonons in solids to atomic Bose-Einstein-condensates Heshami2015 ; Bussieres2013 . Alkali vapor cells are particularly appealing, as they require neither cryogenic temperatures, nor advanced laser cooling techniques, both of which hinder large scale or field applications. Ten millisecond coherence times have been demonstrated in suitable cells Borregaard2016 , and advances up to 100 s are possible with improved anti-relaxation coating technology Balabas2010 , clearly sufficient for most applications. A variety of memory protocols for alkali vapors have been developed Lvovsky2009 , based either on absorption engineering Hosseini2011 , or optically controlled light-matter interaction Kupchak2015 ; Reim2010 ; Shuker2008 . While wavelength matching to QD photons has been achieved Akopian ; Ulrich2014 ; Jahn2015 , a remaining challenge for building a QD compatible atomic memory is that the required acceptance bandwith of $\delta f=$ 0.5 – 1.0 GHz Kuhlmann2015 ; Kuhlmann2013 is rather large compared to the intrinsic linewidth of the alkali D lines, which is on the order of $\delta_{\textrm{Rb}}=5$ MHz Stecka .

One approach to tackle the bandwidth mismatch is to use a far-detuned Raman scheme and dense alkaline vapors Reim2010 . However, this scheme is intrinsically prone to four-wave-mixing (FWM) noise Michelberger2015 , impeding experiments in the quantum regime. Only very recently and with significant technological effort could the FWM problem be circumvented, in an experiment with a cavity-enhanced Raman memory Saunders2015 . While the achieved total internal efficiency was on the order of 10%, the end-to-end memory efficiency was further reduced by about 3 orders of magnitude by the filtering system and impedance matching issues that are hard to avoid in cavity enhanced GHz bandwidth memories Afzelius2010 .

In contrast, we employ a cavity-free near-resonant memory scheme based on electromagnetically induced transparency (EIT) In principle, this scheme can achieve near unity end-to-end efficiencies and sufficient storage bandwidth, while being unaffected by FWM noise Rakher2013 and allowing for spatial multimode operation. For coherent photon wavepackets with FWHM bandwidth of 0.66 GHz we achieve $\eta_{\textrm{e2e}}^{\textrm{50ns}}=3.4(3)\%$ end-to-end efficiency of the fiber-coupled memory, outperforming previous experiments on broadband storage by about two orders of magnitude Saunders2015 , while still leaving plenty of room for future improvements. For a coherent pulse containing one photon on average, the achieved signal to noise ratio is SNR = 3.7(6), demonstrating that FWM noise is indeed suppressed in the EIT memory scheme. We find that EIT-based vapor cell memories are surprisingly well suited for the technologically relevant $\delta f\approx 1$ GHz bandwidth regime, where the storage and retrieval processes are faster than the decoherence rates of the atomic excited states Manz2007 .

We implement the EIT-based memory on the Rb $\textrm{D}_{1}$ line at 795 nm, with the level scheme shown in Fig. 1(a). Initially, all atoms are prepared in the $F=1$ hyperfine state of the $5^{2}S_{1/2}$ ground state manifold by optical pumping. The signal to be stored is generated by a laser red detuned by $\Delta=-2\pi\cdot 0.9$ GHz from the $F=1\rightarrow F^{\prime}=1$, while the control laser is equally detuned by $\Delta$ from the $F=2\rightarrow F^{\prime}=1$ transition. In the experiment signal pulses with a 1 ns fall time from 90% to 10% signal level are generated by modulating an attenuated laser with a fiber-integrated electro-optic modulator, controlled by a fast arbitrary waveform generator, see Fig. 1(b,c). The rise time of the signal is limited to 500 ps by the RF components. The numerical Fourier transform of the measured pulses indicates the FWHM bandwidth of 0.66 GHz. The generated pulses are comparable to the envelope of QD photons, in particular, but not only when photon shaping techniques are applied Beguin2017 . The laser intensity is carefully adjusted such that each pulse in the fiber going into the memory setup contains, on average, $|\alpha|^{2}=1.0(1)$ photon, where the error originates from the uncertainty of the detection efficiency of $\eta_{\textrm{APD}}=60(6)\%$ of the single photon counting avalanche photo diode (APD) used for calibration. To ensure a stable average photon number during the experiments, a constant fraction of the pulse intensity is continuously monitored on a dedicated APD. Similarly, control pulses with Gaussian envelope (FWHM of 5 ns) are generated by modulating a second laser and subsequent amplification in a tapered amplifier (TA). Amplified spontaneous emission from the TA is suppressed by a combination of a narrow band interference filter (0.3 nm FWHM) and a monolithic etalon (finesse 50, 54 GHz free spectral range), allowing for a maximum control power of $120$ mW measured in continuous wave operation. For the Rb $\textrm{D}_{1}$ transition, with a dipole moment of $d=2.54\cdot 10^{-29}$ C$\cdot$m, and the given $e^{-2}$ beam diameter of 525 $\mu$m, this corresponds to a Rabi frequency $\Omega\approx 2\pi\cdot 600$ MHz. The control and signal pulses are combined on a polarizing beam splitter and aligned to enclose an angle of $10(1)$ mrad. This angle is sufficiently small to allow for good overlap between the signal ($e^{-2}$ diameter: 400 $\mu$m) and control beams over the entire vapor cell (length: 37.5 mm). The vapor cell is filled with isotopically enriched 87Rb and 11 Torr (about 15 mbar) N2 buffer gas to reduce radiation trapping and to increase the optical pumping efficiency Thomas2016 . It is heated to 75∘C to achieve an optical depth of OD $=5$ on the $\textrm{D}_{1}$, $F=1\rightarrow F^{\prime}=1$ transition when virtually all atoms are prepared in the $F=1$ ground state.

A major challenge in all quantum memory experiments is the separation of the weak signal from the strong control laser. We apply a combination of polarization filtering, spatial filtering with a single mode fiber, and spectral filtering with a monolithic Fabry-Perot etalon (finesse 50, 27.2 GHz free spectral range). The filtering system suppresses the control beam by more than 12 orders of magnitude (120 dB), while the signal pulses are attenuated by only a factor of 3 (4.8 dB). Signal transmission is mainly limited by optical components without anti-reflection coating, the non-optimized transmission bandwidth of the etalon, and non-ideal mode matching when coupling into fibers, each accounting for about $1.25$ dB signal attenuation.

In a storage and retrieval experiment, the memory is initialized by switching on the control laser for $500$ ns. After a subsequent waiting time of $25$ ns virtually all atoms have been optically pumped into the $F=1$ ground state and the signal and control pulses are sent into the vapor cell. After the storage time $T=50$ ns, a second identical control pulse is applied for readout. Photons at the output fiber are detected with a single photon counting APD (Excelitas, timing resolution 350 ps) and a time-to-digital converter (qutools, timing resolution 81 ps). The experiment is repeated at a rate of $f_{\textrm{rep}}=1.67$ MHz. Figure 2 shows an arrival time histogram of the photons detected during storage and retrieval. Within $t_{\textrm{int}}=1$ s integration time $N_{\textrm{signal}}=42\cdot 10^{3}$ photons are detected within the retrieval window. When the input signal is blocked, $N_{\textrm{noise}}=9\cdot 10^{3}$ photons are detected within the same retrieval window. From this, we infer the noise corrected end-to-end efficiency $\eta_{\textrm{e2e}}^{50\textrm{ns}}=(N_{\textrm{signal}}-N_{\textrm{noise}})/(|\alpha|^{2}\,\eta_{\textrm{APD}}\,f_{\textrm{rep}}t\,_{\textrm{int}})=3.4(3)\%$. The signal to noise ratio for the retrieval of a single photon pulse is $\textrm{SNR }=(N_{\textrm{signal}}-N_{\textrm{noise}})/N_{\textrm{noise}}=3.7(6)$, i.e. for $\mu_{1}=0.27(4)$ input photons the SNR would be unity Jobez2015 .

When correcting for the attenuation of the filtering system, we find an intrinsic memory efficiency of $\eta_{\textrm{int}}^{50\textrm{ns}}=10(2)\%$ for storage and retrieval after $T=50$ ns. The presented memory is not at all optimized for storage time and the $1/e$ memory lifetime is measured to be only $68(7)$ ns. The Gaussian decay of the retrieval signal indicates that atoms diffusing in and out of the narrow interaction volume is the main limitation for the storage time. Due to the high bandwidth of the memory, this comparably low value still allows for a time bandwidth product Nunn2013 on the order of $B=100$. In future experiments, storage lifetime will be extended by several orders of magnitude by using larger beam diameters and magnetic shielding of the vapor cell. When taking the decay of the retrieval signal after 50 ns storage time into account, we find an total intrinsic memory efficiency of $\eta_{\textrm{int}}=17(3)\%$.

To be suitable for quantum applications, it is important that the coherence properties of the light are preserved during the storage process Kupchak2015 . In particular, it is necessary to preserve the mutual coherence between two subsequently stored and retrieved pulses, as well as the second order autocorrelation function of the retrieved signal Sangouard2011 . For measuring coherence between two retrieved pulses, an unbalanced fiber-based Mach-Zehnder interferometer with $400$ ns arm length difference is inserted prior to photon detection. At the same time, the repetition rate for the storage experiment is adjusted to 1/(400 ns) to make the retrieval signal interfere with its time shifted dublicate. Figure 3(a) shows a time trace of the photon flux measured at one interferometer output port, while the interferometer’s phase given by the arm length difference randomly drifts, driven by thermal fluctuations. As compared to the reference signal generated by the input laser pulses, the fringe visibility is reduced to $V=0.65(5)$ for the stored and retrieved light. When increasing the average photon number in the input pulses from $|\alpha|^{2}=1.0$ to $|\alpha|^{2}=10$, almost perfect interference of the retrieved signal with a visibility $V>0.99(1)$ is achieved. This indicates that the reduced visibility in the single photon-level experiment mainly originates in the contamination of the signal by broadband read-out noise that shows no interference, where the SNR = 2 is decreased compared to the measurement shown in Fig. 2. At higher signal intensity the influence of noise photons becomes negligible and consequently almost perfect interference is observed.

The second-order autocorrelation function at zero time delay $g^{(2)}(0)$ of the retrieved photons, measured with a Hanbury Brown and Twiss setup (Fig. 3(b)), shows a slightly increased value of $g^{(2)}(0)=1.3$, compared to the coherent input signal exhibiting $g^{(2)}(0)=1.0$. Again, this is explained by noise contamination: When the input signal is blocked, $g^{(2)}(0)=2.0$ is measured for the readout noise as expected for thermal light. Apart from contamination with broadband fluorescence, the high bandwidth memory preserves coherence and statistical properties of the input state. This is in contrast to previous experiments on low bandwidth memories that are known to be prone to decoherence of the atomic excited state Manz2007 .

To understand the limitations of the present memory experiment, we performed numerical simulations of the system along the lines of Ref. Gorshkov2008 , including Doppler broadening of the atomic transitions by 500 MHz Gorshkov2007a , and the doublet structure of the excited state Rakher2013 . By selection rules, the $m_{F^{\prime}}=0$ Zeeman sub-level of the $F^{\prime}=2$ excited state does not couple to the linearly polarized control laser Yan2001 , which was modeled as a parasitic single-photon transition footnote1 . Dependent on the detuning $\Delta$, up to $\eta_{\textrm{int}}=16\%$ total internal efficiency is predicted for the experimentally realized situation, in excellent agreement with the measured data, see Fig. 4. Using Gaussian control pulses with 4 times higher peak Rabi frequency up to $\eta_{\textrm{int}}=43\%$ can be achieved, while optimal control pulses allow for $\eta_{\textrm{int}}=45\%$. When unwanted excitations of the $F^{\prime}=2,m_{F^{\prime}}=0$ state is prevented $\eta_{\textrm{int}}=60\%$ ($\eta_{\textrm{int}}=92\%$) is predicted for OD = 5 (OD = 35).

In summary, we have demonstrated single-photon-level operation of a technologically simple atomic quantum memory for light pulses with a bandwidth of almost 1 GHz. The pulse intensity and temporal envelopes are comparable to single photons emitted by state-of-the-art semiconductor quantum dot (QD) sources. The memory will be directly suitable as node in a quantum network, if combined with such a source based on GaAs/AlGaAs QDs. Future work will be devoted to achieving storage and retrieval of true single photons emitted by a QD single photon source. The noise level will be reduced by enhancing the pumping efficiency into the $F=1$ ground state over the entire vapor cell, e.g. by using a dedicated pump laser with rather large beam diameter and by using anti-relaxation coated cells. This will prevent atoms in the wrong ground state ($F=2$) from diffusing into the interaction volume and generating readout noise. If necessary, FWM noise can be suppressed by selectively preparing one Zeeman sub-level and exploiting selection rules. The storage time will be extended into the sub-ms regime by increasing the beam diameters (which define the interaction volume) and employing magnetic shielding to reduce ground state decoherence. The memory efficiency will be boosted by optimizing the filtering system and using control pulses with higher power. These straightforward improvements will boost the end-to-end-efficiency to approach $\eta_{\textrm{e2e}}=35\%$. Finally, suppressing the parasitic single-photon transitions by exploiting the Zeeman sub-structure and selection rules and increasing the optical depth will push atomic vapor quantum memories for QD single photons towards unity efficiency, enabling truly scalable quantum networks.

The research leading to these results has received funding from the Marie Skłodowska-Curie Actions of the EU Horizon 2020 Framework Programme under grant agreement No. 702304 (3-5-FIRST) and from the Swiss National Science Foundation via NCCR Quantum Science and Technology.