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The Journal of Chemical Physics

The influence of laser field noise on controlled quantum dynamics

Ignacio R. Solá, HERSCHEL A. RABITZ

Published Apr 28, 2004• 19 citations
Publisher

Abstract

The influence of laser noise on the dynamics of simple quantum systems is analyzed. An anharmonic ladder is chosen for illustration and several pulses are obtained that optimize the yield of a quantum transition by constraining the laser parameters. The following models of laser noise are introduced: Amplitude white noise, phase white noise, frequency white noise and shot-to-shot static noise in the different pulse parameters. It is shown that the optimal pulses are robust to white amplitude noise, since the system acts as a dynamical filter. White phase noise affects the optimal pulses in a similar way by reducing the pulse area. This effect can be easily compensated for by pulse amplitude rescaling, up to a high level of noise. White frequency noise reduces the pulse area and induces spectral broadening, more strongly affecting the high frequency components. It can be partially compensated for by amplitude rescaling. The effects of static noise in the parameters cannot be easily corrected. It is shown that optimal pulses that drive n-photon transitions become more sensitive to noise in the amplitude and less sensitive to noise in the frequency as n increases. The effects of noise in the relative phase rapidly become constant for a large number of interfering pathways.

DOI
10.1063/1.1691803

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The influence of laser noise on the dynamics of simple quantum systems is analyzed. An anharmonic ladder is chosen for illustration and several pulses are obtained that optimize the yield of a quantum transition by constraining the laser parameters. The following models of laser noise are introduced: Amplitude white noise, phase white noise, frequency white noise and shot-to-shot static noise in the different pulse parameters. It is shown that the optimal pulses are robust to white amplitude noise, since the system acts as a dynamical filter. White phase noise affects the optimal pulses in a similar way by reducing the pulse area. This effect can be easily compensated for by pulse amplitude rescaling, up to a high level of noise. White frequency noise reduces the pulse area and induces spectral broadening, more strongly affecting the high frequency components. It can be partially compensated for by amplitude rescaling. The effects of static noise in the parameters cannot be easily corrected. It is shown that optimal pulses that drive n-photon transitions become more sensitive to noise in the amplitude and less sensitive to noise in the frequency as n increases. The effects of noise in the relative phase rapidly become constant for a large number of interfering pathways.
We investigate the influence of pump bandwidth and pump intensity noise on the quantum-noise properties of lasers based on a Raman atomic-gain medium, which recently have been predicted to emit narrow-bandwidth, sub-shot-noise light. We show that, using finite-bandwidth pump light, the predicted limit to the laser bandwidth can still be well below the value given by the Shawlow-Townes formula and much smaller than the input bandwidth. The laser intensity noise is shown to be relatively insensitive to input phase noise as long as the Rabi frequency on the lasing transition is large compared to the bandwidth. On the other hand, even small amounts of pump amplitude noise tend to increase strongly the laser spectral bandwidth, especially in the high-intensity limit. Including dynamic pump-noise reduction through multilevel atomic cycling in our model leads to a Mandel Q parameter value even below Q=-1/2, together with a significant enhancement of the output intensity-noise squeezing.
We discuss recent advances in optimal control theory (OCT) related to the investigation of the impact of control field noise on controllability of quantum dynamics. Two numerical methods, the gradient method and the iteration method, are paid particular attention. We analyze the problem of designing noisy control fields to maximize the vibrational transition probability in diatomic quantum systems, e.g. the HF and OH molecules. White noise is used as an additive random variable in the amplitude of the control field. It is demonstrated that the convergence is faster in the presence of noise and population transfer is increased by 0.04% for small values of noise compared to the field amplitude.
The mechanism for quantum noise suppression in a multimode laser with a homogeneously broadened line is explained. It is shown that the spontaneous emission noise and pump noise contribution to the photon number fluctuations inside the laser cavity may be suppressed infinitely (up to their complete elimination) when the number of modes participating in the generation is increased. Low-frequency spectral squeezing for an individual output field mode in optimal conditions tends to 100% as the total number of modes increases. The low-frequency spectral squeezing for the total output field may reach 50% below the shot noise level under optimal conditions. The noise suppression of the laser light is explained by the saturation effect of an atomic transition and inter-mode correlation. A multimode laser is an accessible source of light with potentially fully suppressed quantum noise.
Understanding and mitigating noise in two-level quantum systems is essential for achieving high-fidelity qubit control. Conventional frequency tracking techniques, such as Ramsey interferometry, are fundamentally limited by trade-offs between sensitivity, bandwidth, and dynamic range. Here we introduce the adiabatic tangentially-modulated (ATM) pulse, a pulse derived from quantum adiabatic theory that maps qubit detuning onto a sigmoidal, near-binary response. Using numerical simulations supported by analytical modeling, we show that pulse sensitivity and detuning range can be independently engineered through simple design parameters. We derive scaling relations governing these quantities and demonstrate their agreement with simulation. A single-shot ATM measurement achieves sensitivity comparable to that obtained from multi-shot Ramsey averaging, enabling tracking of substantially higher frequency noise components with a lower closed-loop white-noise floor. In addition, this pulse exhibits strong robustness to amplitude fluctuations compared with binary response pulses derived from the Shinnar-Le Roux formalism. Together, these properties establish the ATM pulse as a promising approach for robust qubit frequency tracking.
Current laser systems have phase and amplitude fluctuations which are partially quantum in origin. The amplitude fluctuations of a highly stabilized laser are shot noise limited, that is they have quantum fluctuations due to the Poissonian fluctuations of photons in a coherent state. These photon number fluctuations have been shown to have an origin in the incoherent pumping mechanism used for standard lasers. It has recently been demonstrated experimentally that by suppressing the amplitude fluctuations of the pump a laser output with reduced amplitude fluctuations is possible. The phase fluctuations in a laser are due to phase diffusion and are substantially above the quantum limit. Techniques to reduce the laser phase fluctuations have been proposed making use of correlated spontaneous emission.
We present a comprehensive theoretical analysis of ultrafast entanglement generation between two Rydberg-blockaded atoms, explicitly accounting for realistic laser noise. Using femtosecond Gaussian pulses as a baseline, we systematically evaluate Bell-state fidelity sensitivity to amplitude and phase noise across white, pink (1/f), and Ornstein-Uhlenbeck spectra using Monte Carlo ensemble simulations. Our results show that amplitude noise is well tolerated, with fidelities above 90% even at 30% noise levels, while phase noise is the primary limiting factor, causing fidelity to drop rapidly beyond about 1% noise amplitude. The spectral structure of the noise is also important: pink noise consistently causes less fidelity loss than white noise of the same amplitude. By applying quantum optimal control theory (QOCT) with the D-MORPH algorithm under multiple equality constraints, we obtain a double-pulse structure with a spectral notch that achieves approximately 99% fidelity in the noise-free case and maintains high fidelity under moderate amplitude noise. A breakdown threshold near 1% amplitude noise is identified, beyond which even optimized pulses cannot sustain coherent control. These results offer practical benchmarks for the development of ultrafast neutral-atom quantum processors operating in the femtosecond regime.