Memory Device for Photons by exploiting Brillouin Interactions in Nanowires

Technical Summary: Memory Device for Photons by Exploiting Brillouin Interactions in Nanowires

Problem Statement
The storage of optical signals at the single-photon level is a critical requirement for quantum information processing and communications. While significant progress has been made in optical storage using techniques like whispering gallery mode resonators and optomechanical cavities, and while coherent buffer approaches using Stimulated Brillouin Scattering (SBS) in integrated waveguides have been demonstrated, existing methods face limitations when applied to single-photon signals. Specifically, standard SBS memory schemes rely on converting an optical signal into a long-lived acoustic excitation. However, the finite lifetime of these acoustic waves (determined by the phonon damping rate $\Gamma$) and the presence of thermal phonons impose strict constraints. The paper argues that for signals containing only a few or single photons, the dissipation of the acoustic excitation and the noise introduced by thermal phonons render the standard "write-store-retrieve" conversion approach inefficient or inapplicable.

Methodology
The paper investigates two distinct configurations for storing light within nanoscale dielectric waveguides (nanowires) where the transverse dimension $d$ is comparable to the light wavelength $\lambda$. The study utilizes a microscopic quantum theory of photon-phonon interactions mediated by SBS, accounting for both electrostriction and radiation pressure mechanisms.

1. Configuration 1: Coherent Buffer via Acoustic Conversion
   The authors first analyze the standard approach where an optical signal pulse is coherently converted into an acoustic wave (phonon) via interaction with a counter-propagating "write" control pulse. The signal is retrieved later by a "read" control pulse. The dynamics are modeled using coupled equations of motion for the signal field amplitude and the phonon field, incorporating phenomenological damping rates ($\Gamma$ for phonons, $\gamma$ for photons). The study employs the quantum Langevin method to explicitly calculate the impact of thermal phonons on the signal, deriving the average number of spurious signal photons ($N_f$) generated by the scattering of pump photons off thermal phonons.

2. Configuration 2: Slow Light via Dual-Pump Brillouin Scattering
   To overcome the limitations of acoustic lifetime and thermal noise, the paper introduces a second configuration based on "slow light." In this scheme, a signal field is coupled to two counter-propagating classical pump fields (an upper pump at frequency $\omega_u$ and a lower pump at $\omega_l$) via SBS.

   • The system is modeled using Heisenberg-Langevin equations for the signal photon operator and two phonon operators (corresponding to the two scattering processes).
   • The analysis focuses on achieving a regime where the effective gain ($G$) is negligible ($G \approx 0$) to prevent amplification or attenuation, while simultaneously achieving a significantly reduced effective group velocity ($v_e \ll v_g$).
   • The authors derive conditions for the pump intensities and detunings required to balance the gain and phase shifts, ensuring the signal propagates without loss while being slowed down. They also calculate the contribution of thermal fluctuations to the signal amplitude in this regime.

Key Contributions and Results

• Limitations of Acoustic Conversion: The paper confirms that the standard SBS memory device works efficiently for optical pulses with a high average number of photons. However, for single-photon signals, the requirement that the storage time $\Delta$ be shorter than the phonon lifetime ($1/\Gamma$) severely limits the storage duration. Furthermore, the analysis of thermal phonons shows that for single-photon signals, the condition $N_f \ll 1$ (where $N_f$ is the number of scattered photons induced by thermal fluctuations) is difficult to satisfy with standard parameters, effectively forbidding the storage of single photons via this conversion method.
• Feasibility of Single-Photon Slow Light: The proposed dual-pump configuration successfully demonstrates a mechanism to slow down single-photon signals without gain or loss. By balancing the scattering from the upper pump (which tends to amplify the signal) and the lower pump (which tends to attenuate it), the authors derive a condition where the net gain is zero.
• Quantitative Performance: Using physical parameters typical for nanowires (e.g., coupling strength $g = 10^6$ Hz, phonon damping $\Gamma = 10^8$ Hz, wire length $L=1$ cm), the model predicts a reduction in effective group velocity by several orders of magnitude (e.g., $v_e/v_g \approx 10^{-4}$). This results in a time delay on the order of microseconds ($\Delta t \approx 1 \mu s$) for a 1 cm wire.
• Thermal Noise Suppression: Crucially, the paper derives the condition under which thermal fluctuations are negligible ($N_{out} \ll 1$). Under the derived optimal parameters (specific pump intensity ratios and detunings), the contribution of thermal phonons to the signal is calculated to be approximately $2.8 \times 10^{-3}$, satisfying the requirement for single-photon operation.

Significance and Claims
The paper claims to address the specific obstacle of thermal phonons and acoustic damping that prevents the storage of single photons in standard SBS memory devices. By shifting the paradigm from "converting light to sound" to "slowing light via sound-mediated interactions," the authors propose a viable configuration for a photonic memory device that operates at the single-photon level.

The significance lies in the demonstration that:

1. Nanoscale waveguides can support photon-phonon coupling strong enough to manipulate single photons.
2. A "slow light" configuration using two counter-propagating pumps can achieve significant time delays (storage) without the signal being lost to damping or corrupted by thermal noise.
3. This approach provides a potential physical implementation for quantum information processing components (memory/buffers) that are compatible with on-chip integration and do not require the signal to be converted into a long-lived mechanical excitation, thereby bypassing the lifetime limitations of acoustic waves.

The authors conclude that while the first scenario (acoustic conversion) is limited to high-photon-number signals, the second scenario (slow light) is suitable for single-photon signals, making it a promising candidate for quantum communication and processing applications.