A light pulse can be stopped and stored as an atomic spin-wave imprint in one Bose–Einstein condensate (BEC), converted into a travelling 'messenger' matter wave, and coherently revived as light from a second, spatially separated condensate, as demonstrated by Ginsberg, Garner and Hau (Nature 445, 623–626; 2007). That demonstration was a one-shot, classical proof of principle: roughly half of the pulse energy was lost during slow-light propagation before storage, additional amplitude was lost to atom–atom scattering in the messenger pulse, storage/flight times were at the millisecond scale, and the two condensates had a random relative phase, ruling out deterministic interferometric readout. The open problem is to turn this matter-wave-mediated optical channel into a genuinely coherent information processor: quantitatively minimize both loss channels, increase the optical bandwidth and delay–bandwidth product, extend storage times, lock or control the relative phase between sender and receiver condensates for deterministic interferometry, and map classical and non-classical (quantum) states of a stored messenger pulse onto revived light fields, with quantified fidelities for repeated or multiplexed transfers.

Background

In electromagnetically induced transparency (EIT), two laser fields (a 'probe' and a 'coupling' beam) drive atoms in a three-level lambda configuration into a coherent superposition of two stable ground states – a 'dark state' in which excitation amplitudes destructively interfere so that neither beam is absorbed. Near two-photon resonance the probe experiences a steep, rapidly varying refractive index, so a probe pulse propagating through the medium is slowed by many orders of magnitude and spatially compressed; in a Bose–Einstein condensate (BEC), a macroscopically occupied quantum gas in which thermal diffusion is absent, light was slowed to 17 m/s (Hau et al., 1999) and halted and stored as a collective atomic spin-wave imprint by turning the coupling field off adiabatically (Liu et al., 2001). The dark-state ratio ties the amplitude and phase of the stored atomic component in the second ground state to those of the probe field, so storage and retrieval preserve the optical information. Ginsberg, Garner and Hau (2007) added a crucial ingredient: the anti-parallel geometry of probe and coupling beams imprints a two-photon recoil momentum on the stored atomic component, so the imprint – the 'messenger' atom pulse in state ∣2⟩|2\rangle – is ballistically ejected from the storing condensate and travels as a coherent matter wave. When it arrives at a second, spatially separated condensate in state ∣1⟩|1\rangle (160 µm away in the experiment), re-illuminating the system with the coupling laser drives the probe pulse back on through slow-light-mediated bosonic matter-wave amplification: scattering of messenger atoms into the macroscopically occupied ∣1⟩|1\rangle condensate mode is bosonically stimulated, which secures coherence during regeneration of the light. The revived pulse was observed after messenger flights of a few milliseconds, and pulses could be revived within a single condensate up to 0.7 ms after storage; the decay of revival energy in a thermal (non-condensed) cloud, by contrast, occurs on a 2.5 ms scale over distances of order the thermal de Broglie wavelength. The achievable delay–bandwidth product in the experiment was already of order 10310^3–10410^4. The authors identified the loss budget (about 50% of the pulse energy lost to slow-light propagation before storage, plus loss of ∣2⟩|2\rangle messenger amplitude to atom–atom scattering) and pointed to atomic-species and magnetic-sublevel selection and scattering-length manipulation (for example with Feshbach resonances, i.e. magnetic-field-tuned molecular resonances that alter interatomic scattering lengths), as well as density-profile shaping of the ∣1⟩|1\rangle condensates, as routes to higher efficiency, bandwidth, and larger delay–bandwidth. Because the two condensates in the experiment were prepared independently, their relative phase was completely random: interference of a revived pulse with a reference pulse would show high contrast but a random absolute fringe position, so deterministic interferometry requires phase-locked or phase-controlled sender–receiver pairs. The authors further proposed that the messenger pulse, travelling in free space, could be independently trapped – potentially for minutes – and manipulated, that classical and quantum states of the trapped pulse could then be mapped onto revived light fields, that repeated condensate-to-condensate transfer could replenish a continuous atom laser, and that the revival geometry itself forms a new interferometer in which spatially selected parts of an atomic wavefunction interfere, usable for measuring off-diagonal long-range order (the macroscopic phase coherence of a quantum gas, i.e. long-range one-body coherence) in spatially selected regions of degenerate gases of bosons and fermions. The same group later showed (Zhang, Garner and Hau, 2009) that in a single optically trapped condensate, controlling both the real and imaginary parts of the scattering lengths and letting the stored imprint phase-separate into a self-induced void extends classical storage times beyond one second – implementing the scattering-control strategy, but in a single-trapped-BEC storage architecture rather than the two-condensate messenger-transfer geometry, and leaving the phase-referenced and quantum-state-mapping questions untouched. Quantum-domain (single-photon-level) storage in a BEC was achieved only much later (Saglamyurek et al., 2021) with the Autler–Townes-splitting memory protocol (a quantum-memory scheme in which a strong coupling field splits the atomic absorption line into a doublet, so that a pulse fits into the gap between the two peaks and is stored as an atomic coherence), but with a lifetime of only microseconds and no matter-wave messenger transfer. Controlled spatial displacement of stored light has meanwhile been demonstrated by a different, non-BEC route: frequency-controlled transport of the stored spin wave over 1.2 mm in a cold-atom EIT memory (Li, Islam and Windpassinger, 2020), and at room temperature in 2025.

Problem Statement

As demonstrated in 2007, a classical light pulse can be stored in one Bose–Einstein condensate (BEC), carried as a coherent 'messenger' matter-wave pulse in internal state ∣2⟩|2\rangle to a second BEC, and revived there as light. Making this matter-wave-mediated optical channel a practical, coherent information processor remains open. The single overarching objective is a phase-coherent, low-loss, long-duration, quantum-capable transfer of optical information between condensates via matter-wave dynamics, with the following jointly supporting deliverables: (1) quantitatively minimize and characterize the two identified loss channels – the ~50% energy loss during ultraslow-light propagation before storage and the loss of ∣2⟩|2\rangle messenger amplitude to atom–atom scattering – in the transfer geometry itself; (2) increase the optical bandwidth and delay–bandwidth product of the process while suppressing propagation loss in the ∣1⟩|1\rangle receiver condensates; (3) extend the storage time beyond the demonstrated approximately 0.7 ms (single condensate) and few-ms messenger flight, and quantify the preservation of coherence over that extended storage; (4) replace the random relative phase of independently prepared condensates with phase-locked or phase-controlled sender–receiver pairs, enabling deterministic interferometric readout of the revived light (high-contrast interference with a fixed fringe position), and thereby realize the proposed new interferometer in which spatially selected parts of an atomic wavefunction interfere, including its use for measuring off-diagonal long-range order in spatially selected regions of degenerate gases of bosons and fermions; and (5) establish the fidelity limits of repeated and multiplexed transfers (for example, repeated replenishing of an atom laser via successive messenger pulses) and demonstrate the mapping of non-classical quantum states of a trapped messenger pulse onto revived light fields. The objective is to demonstrate and quantitatively characterize these five capabilities in the condensate-based matter-wave-messenger geometry, rather than in alternative storage architectures. Each of the five capabilities is delimited by the corresponding baseline of the 2007 demonstration (the ~50% pre-storage slow-light loss and messenger atom–atom scattering loss; the 10310^3–10410^4 delay–bandwidth product; the approximately 0.7 ms single-condensate revival and millisecond-scale messenger flight; the random sender–receiver relative phase; and the unquantified repeated-transfer and non-classical-state fidelities). Each capability bundled inside deliverable (4) (deterministic phase-referenced interferometric readout; its off-diagonal-long-range-order application) and inside deliverable (5) (fidelity of repeated or multiplexed transfers; mapping of non-classical quantum states onto revived light) is separately required, and neither capability implies its partner.

References

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