Optically Writable Atomic Vapor Memory as a Substrate for Optical Reservoir Computing

Elizabeth Robertson; Mingwei Yang; Lina Jaurigue; Guillermo Gallego; Kathy Lüdge; Janik Wolters

physics.atom-phAug 18, 2026

Optically Writable Atomic Vapor Memory as a Substrate for Optical Reservoir Computing

Authors: Elizabeth Robertson, Mingwei Yang, Lina Jaurigue, Guillermo Gallego, Kathy Lüdge, Janik Wolters

Organizations: Institute of Space Research, German Aerospace Center (DLR), Berlin, Germany · Institute of Physics, Technische Universität Berlin, Berlin, Germany · Institut für Physik, Technische Universität Illmenau, Illmenau, Germany · Department of Electrical Engineering and Computer Science, Technical University of Berlin, Berlin, Germany ·

Abstract

We present an optical random access memory (ORAM) based on warm cesium (Cs) atomic vapor and demonstrate its operation as the physical substrate of a reservoir computer. Information is stored in the hyperfine population distribution of a Cs ensemble via optical pumping and retrieved through differential probe absorption. Spatial multiplexing via acousto-optic deflection provides eight addressable memory rails able to store up to 3.8 bits of information per rail. Employing this platform as a temporally multiplexed reservoir, we achieve a kernel rank ( $\mathrm{KR}= 8.8 \pm 0.4$ ), and a minimum bit error rate of $0.02 \pm 0.01$ on the Exclusive-or (XOR) benchmark. We find the limited memory lifetime constrains the achievable temporal depth, encouraging further research into fast addressable memories. This constitutes the first demonstration of a free-space, optically writable atomic RAM as a substrate in an optical reservoir computing system.

Figures & tables

Figure 1: Operating principle of the incoherent atomic ORAM. (a) A strong pump pulse transfers atoms to the dark state

|g\rangle

, rendering the medium transparent to a subsequent weak probe. (b) A weaker pump transfers fewer atoms, yielding lower probe transmission. The stored analog value is encoded in the measured probe intensity.

Figure 2: a) Experimental setup of the Cs ORAM. The laser is frequency-locked via Doppler-free spectroscopy (dashed box). After magnification from lenses L1 and L2, the pump/probe beam is diffracted by AOM1 into

N

spatial rails that traverse the Cs cell; AOM2 recombines the modes onto a single detector path. FC: Fiber coupler; L: Lens; DET: Detector; AWG: arbitrary wave generator; PBS: polarizing beamsplitter; BB: beam block; M: mirror; RP: Red Pitaya; WP: waveplate;

\lambda/2

: half-wave plate;

\lambda/4

: quarter-wave plate. b) Single-rail pump-probe timing sequence. AOM2 is turned off during pumping to prevent damage to the detector.

Figure 3: Characteristic memory responses (a) Saturation absorption transfer function of the eight ORAM rails. Experimental data are fit with a saturable absorber profile, which defines the nonlinear function

\theta

used in reservoir simulations. Mean saturation power:

P_{\mathrm{sat}}=1.5~

mW. (b) Decay of atomic polarization for pump durations

t_{\mathrm{pump}}\in\{10,20,50,100,200\}~\mu

s at

P_{\mathrm{pump}}=1.5~

mW. The peak feature at

t=0

is leaked pump light indicating the switch from the pump to the probe pulse. Inset: Measured

T_{1}

vs.

t_{\mathrm{pump}}

, fit with

T_{1}=a(1-e^{-kx})+b

; the curve saturates at approximately

1~

ms for

t_{\mathrm{pump}}\geq 200\,\mu

Figure of merit	Value
Memory lifetime ( $T_{1}$ )	$230\,\mathrm{\mu s}$
Resolution	3.8 bits
Number of rails ( $N$ )	8
Read/write duration ( $t_{\mathrm{pp}}$ )	$30\,\mathrm{\mu s}$
Memory bandwidth ( $\mathrm{TBP}_{\mathrm{mem}}$ )	7.7

Table 1: The key characteristics of the incoherent memory experiment.

Figure 4: Schematic of the memory-based reservoir computer. At each time step, the memory rails are first probed (read) before being pumped (written). The coupling matrices

\mathbf{K}_{\mathrm{in}}

and

\mathbf{K}_{\mathrm{out}}

determine which rails are addressed, establishing the effective network topology.

Figure 5: Linear memory capacity as a function of virtual node number $N_{v}$ and $\mathrm{TBP}_{\mathrm{mem}}$ , for $T_{1}=230~\mu$ s ( $t_{\mathrm{pump}}=10~\mu$ s), $g_{1}=1$ . (a) Simulation; (b) experiment. The experimentally scanned region is indicated in green. The maximum experimental MC $=1.0\pm 0.2$ is achieved at $N_{v}=14$ , $\mathrm{TBP}_{\mathrm{mem}}=3.8$ .

Figure 6: Kernel rank as a function of $N_{v}$ and $\mathrm{TBP}_{\mathrm{mem}}$ for $T_{1}=230~\mu$ s. (a) Simulation, KR ${}_{\mathrm{sim}}^{\mathrm{max}}=7.8\pm 0.4$ ; (b) experiment, KR ${}_{\mathrm{exp}}^{\mathrm{max}}=8.8\pm 0.4$ .

Figure 7: Simulated kernel rank as a function of input scaling $g_{1}$ and $\mathrm{TBP}_{\mathrm{mem}}$ for $N_{v}=11$ , $T_{1}=230~\mu$ s. $g_{1}<1$ restricts pumping to the linear regime. The KR range spans $6.8$ – $8.0$ , with no strong dependence on $g_{1}$ .

Figure 8: (a) Simulated and (b) experimental XOR performance (BER) as a function of $N_{v}$ and $\mathrm{TBP}_{\mathrm{mem}}$ for $T_{1}=230~\mu$ s, $g_{1}=1$ . In simulation $\mathrm{BER_{\mathrm{sim}}^{\text{(min)}}}=0$ , for $N_{v}\in\{8,12,14\}$ , for all values of $\text{TBP}_{\text{mem}}$ , except $\text{TBP}_{\text{mem}}=7.7$ . The lowest experimental accuracy is $\mathrm{BER}_{\mathrm{exp}}^{\text{(min)}}=0.03(3)$ is obtained at $N_{v}=12$ , $\text{TBP}_{\text{mem}}=6.4$ .

Figure 9: XOR performance (BER) as a function of input scaling $g_{1}$ and $\mathrm{TBP}_{\mathrm{mem}}$ for $N_{v}=12$ , $T_{1}=230~\mu$ s. (a) Simulation: BER $=0$ across all $g_{1}$ for $\mathrm{TBP}_{\mathrm{mem}}\geq 4.8$ . (b) Experiment: minimum BER $=0.02(1)$ at $g_{1}=0.6$ , $\mathrm{TBP}_{\mathrm{mem}}=6.4$ .

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Universal approximation in reservoir computing is typically associated with a class of reservoirs. We show that universality can be associated with a single reservoir, considering a minimal setup of a single atom in front of a mirror. In its linear-transducer limit, our reservoir is a universal approximator of fading-memory maps under an operating class of checkable conditions, with a rate constant measured at the operating point. A given reservoir can reach arbitrary accuracy by changing measurement settings. The proof gives an explicit recipe: for a target accuracy, it specifies the required physical resources and resonator modes. Enlarging the number of accessible modes increases the matchable kernel span without reducing capability. Beyond the linear limit, the atom's saturation replaces high-order polynomial readouts, and the device operates on real-world tasks alongside classical baselines. Our results highlight an example of universality with a minimal quantum setup.

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