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Physica Scripta

Spatial-temporal quantum optical pulses in stimulated raman quantum memory with laser-controlled dynamical stark and generalized quantum noise operators

C. H. Raymond Ooi, Shreyes Subramaniam

Published Dec 1, 2025• 0 citations
Publisher

Abstract

Abstract Stimulated Raman scattering (SRS) is highly relevant to quantum memories involving Raman system. Using quantum Langevin equations with complete noise operators coupled to the quantum field propagation equation, we present a general theory of SRS for moving quantum particles where quantum Stokes pulse couples to both transitions (m1 and m3) while an arbitrary laser pulses couple to only one (m1) transition. Our coupled equations contain dynamical ac Stark shift due to laser pulses and Doppler shift, complete quantum noise operators and atomic coherences corresponding to all possible three transitions (not only the ground state coherence), quantum mechanical microscopic expressions for linear and nonlinear interactions with nonlocal (memory) or temporal dispersion effects. We obtain an analytical solution of the quantum Stokes field in laboratory spacetime with generalized quantum noise operators that include all initial atomic coherences and arbitrary initial and boundary quantum fields, valid for arbitrary laser pulses. The general solution provides a complete physical picture, composed of basically two parts: above and below the light line, t = z/c. This robust framework offers a powerful tool for optimizing Raman-based quantum information processes, particularly for modeling the spatial-temporal dynamics of quantum Stokes pulses in storage and retrieval stages of quantum memory.

DOI
10.1088/1402-4896/ae2c63

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Abstract Stimulated Raman scattering (SRS) is highly relevant to quantum memories involving Raman system. Using quantum Langevin equations with complete noise operators coupled to the quantum field propagation equation, we present a general theory of SRS for moving quantum particles where quantum Stokes pulse couples to both transitions (m1 and m3) while an arbitrary laser pulses couple to only one (m1) transition. Our coupled equations contain dynamical ac Stark shift due to laser pulses and Doppler shift, complete quantum noise operators and atomic coherences corresponding to all possible three transitions (not only the ground state coherence), quantum mechanical microscopic expressions for linear and nonlinear interactions with nonlocal (memory) or temporal dispersion effects. We obtain an analytical solution of the quantum Stokes field in laboratory spacetime with generalized quantum noise operators that include all initial atomic coherences and arbitrary initial and boundary quantum fields, valid for arbitrary laser pulses. The general solution provides a complete physical picture, composed of basically two parts: above and below the light line, t = z/c. This robust framework offers a powerful tool for optimizing Raman-based quantum information processes, particularly for modeling the spatial-temporal dynamics of quantum Stokes pulses in storage and retrieval stages of quantum memory.
Abstract We present a generalized quantum theory of stimulated Raman scattering, which is based on coupled Heisenberg–Langevin equations. Analytical solutions in previous models neglect the effects of the frequency dispersion, assume far-off resonance and only consider slowly varying terms in the atomic operator. In obtaining the more general theory, we have derived partial integro-differential equation containing polarization kernels that include all the temporal nonlocal effects using systematic integral method over time. Analytical solutions of the Stokes field with greater generality for arbitrary spatial-temporal laser fields have been obtained using Laplace transform in the retarded space frame with minimal approximations made. The solutions are very general and potentially useful for studying systems in which highly accurate modeling is required such as quantum memories of a wide range of Raman systems.
A quantum theory of stimulated Raman scattering is established that takes into account the time-dependence of pump laser pulse, two-photon detuning and atomic populations, allowing the general transient and spatial propagation study of Raman memory. Heisenberg–Langevin and Maxwell equations for the collective atomic operators are solved analytically under adiabatic condition , where the electric field envelopes and the collective atomic operators vary slowly. The analytical solution of Stokes/anti-Stokes signal electric field operator is obtained. The spatial–temporal intensity of quantum signal field is studied numerically and analytically for different two-photon detunings and initial populations.
A pencil shaped region of a Raman-active medium forms a source for Stokes-shifted light via stimulated Raman Scattering (SRS) when driven by an intense laser pulse. Stokes photons are scattered spontaneously at first, and then amplified during propagation through the medium. Since the scattering is initiated by quantum noise, the actual number of photons produced in any given pulse will be highly uncertain, even if the pulse energy of the driving laser is constant1. As the Stokes light propagates through such an extended region, it's coherence properties will be changed. The spatial coherence is determined by the size and shape of the region, which may be characterized by its Fresnel number F, defined as F= A/λSL, where A is the cross-sectional area of the interaction region, which has length L, and λS is the Stokes wavelength. The rate at which the microscopic scatterers (atoms or molecules) are dephased by collisions affects the temporal coherence of the Stokes light, characterised by the temporal coherence parameter Γτ /gL, where Γ is the collisional dephasing rate, τ is the laser pulse duration and g is the steady-state Raman gain coefficient.
A theory of stimulated Raman scattering (SRS) is presented which treats in a unified manner the buildup of SRS from spontaneous Raman scattering and the spatial propagation which leads to gain. Maxwell-Bloch equations describe the coupling between the Stokes field operator and the collective atomic operators, which are driven by a classical laser field under low-signal-gain conditions, where the atomic ground states and laser field remain undepleted. An analytic expression is derived for the forward-propagating Stokes field operator in a one-dimensional spatial approximation when the Fresnel number of the excited medium is unity. Steady-state and transient Stokes intensities are evaluated under low-gain (spontaneous) and high-gain (stimulated) conditions. The Stokes intensity is found to be exactly independent of a laser bandwidth arising solely from phase fluctuations. The power spectrum of steady-state SRS is evaluated, giving a gain-narrowed spectral profile when the laser is narrow band, and a spectrum identical to the laser spectrum when the laser is broad band. A strong analogy between SRS and two-level superfluorescence is found; in both cases the macroscopic, collective dipole moment is initiated by quantum fluctuations.
A quantum theory of stimulated Raman scattering is presented that takes into account three-dimensional propagation and collisional dephasing, allowing the study of the spatial and temporal coherence properties of the generated Stokes light. Maxwell-Bloch equations for the Stokes field operator and the collective atomic operators are solved analytically under low-signal-gain conditions, where the laser field and the atomic ground states remain undepleted. The intensity and the space-time autocorrelation function of the Stokes field are calculated. The Stokes field is expanded into a set of statistically independent ``coherence modes,'' which are determined explicitly for the case of a cylindrically shaped pumped volume. The Stokes pulse energy W is found to fluctuate from pulse to pulse. The probability distribution function for pulse energies P(W) is calculated for a range of Fresnel numbers of the excited volume and collisional dephasing rates. For small values of Fresnel number and dephasing rate, P(W) is a negative exponential distribution. For large values of either, P(W) narrows and approaches a Gaussian-shaped distribution. This occurs because many independent modes contribute to the Stokes emission, making it spatially and/or temporally incoherent.
From a classical point of view the generation of Stokes light by stimulated Raman scattering (SRS) is not possible unless a Stokes input signal is supplied. On the other hand, the gain in SRS can be so large that without input the spontaneous build-up of strong Stokes waves can be observed. A proper quantum theoretical description1 shows that this spontaneous initiation of Stokes generation is due to microscopic random fluctuations originating from quantum noise associated with the dynamical variable Q(t) which is active in the Raman process, e.g., a molecular normal mode coordinate. In highly transient SRS -when the duration of the excitation pulse is shorter than the dephasing time- the Stokes field is proportional to the initial Heisenberg operator Q(0) describing the state of the system just before the excitation pulse is turned on (t=0). In this case the statistics of the final Stokes pulse energy is determined by quantum mechanical uncertainties associated with the random Raman polarization of the initial state2. On the other hand, in a steady state situation the Stokes pulse fluctuations are substantially reduced and the Stokes pulse energy is stabilized as a result of damping processes.