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arXiv:2508.07890

On the relationship between noise squeezing and Rabi oscillations in active quantum dot ensembles

Ori Gabai, A. Willinger, Igor Khanonkin, Vitalii I. Sichkovskyi, Johann Peter Reithmaier, Gadi Eisenstein

Published Aug 11, 2025• 0 citations
arXivHTMLPDF

Abstract

Squeezed light is usually generated using passive nonlinear materials. Semiconductor lasers and optical amplifiers (SOAs) also offer nonlinearities but they differ in that they add amplified spontaneous emission (ASE). Squeezing to below the vacuum level has been demonstrated in a semiconductor laser, and gain saturation in SOAs can likewise reduce photon-number fluctuations to, and in some cases below, the vacuum limit. Here, we demonstrate that Rabi oscillations in room-temperature quantum-dot SOAs, induced by short resonant pulses, cause cyclical noise modification that repeat with every change of 2pi in pulse area, corresponding to a fourfold increase in excitation pulse energy. Homodyne measurements reveal in those cases elliptical Wigner functions corresponding to squeezed thermal states and in certain regimes, the state is squeezed to below the vacuum level. At other pulse areas, the Wigner functions are circular representing thermal coherent states. This periodic behavior persists over two orders of magnitude in input pulse energy, spanning several 2pi cycles. Under specific bias and excitation conditions, we further observe a non-Gaussian Wigner function featuring two bright lobes. Although its precise nature remains unresolved, this structure may be consistent with a Schrodinger cat - like state whose accompanying negativity is suppressed due to an approximately 10 dB optical output loss. Notably, the emergence of this non-Gaussian state is itself periodic in excitation pulse energy.

DOI
10.48550/arxiv.2508.07890

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Squeezed light is usually generated using passive nonlinear materials. Semiconductor lasers and optical amplifiers (SOAs) also offer nonlinearities but they differ in that they add amplified spontaneous emission (ASE). Squeezing to below the vacuum level has been demonstrated in a semiconductor laser, and gain saturation in SOAs can likewise reduce photon-number fluctuations to, and in some cases below, the vacuum limit. Here, we demonstrate that Rabi oscillations in room-temperature quantum-dot SOAs, induced by short resonant pulses, cause cyclical noise modification that repeat with every change of 2pi in pulse area, corresponding to a fourfold increase in excitation pulse energy. Homodyne measurements reveal in those cases elliptical Wigner functions corresponding to squeezed thermal states and in certain regimes, the state is squeezed to below the vacuum level. At other pulse areas, the Wigner functions are circular representing thermal coherent states. This periodic behavior persists over two orders of magnitude in input pulse energy, spanning several 2pi cycles. Under specific bias and excitation conditions, we further observe a non-Gaussian Wigner function featuring two bright lobes. Although its precise nature remains unresolved, this structure may be consistent with a Schrodinger cat - like state whose accompanying negativity is suppressed due to an approximately 10 dB optical output loss. Notably, the emergence of this non-Gaussian state is itself periodic in excitation pulse energy.
We study experimentally and numerically the changes in pulse shape a Gaussian laser pulse undergoes when propagating through an electrically pumped quantum dot semiconductor optical amplifier (QD-SOA). The pulse energy is set to be resonant to the quantum dot ground state transition, and the pulse shape is analyzed in phase and amplitude in a heterodyne cross-correlation experiment. For the case of an inverted system, we observe the appearance of a periodic modulation of the temporal pulse profile above a critical pulse power. Similar signatures of pulse break-up have been observed at low temperature in quantum dot ensembles without electrical pumping and were linked to optically induced Rabi oscillations imprinting the coherent switching between absorption and stimulated emission of photons by the material system.
Amplitude-squeezed states are produced from a room-temperature Fabry-P\'erot quantum-well semiconductor laser using a combination of pump suppression and weak, dispersive optical feedback. Up to 0.9 dB of squeezing is measured using a balanced homodyne detector corresponding to 1.5 dB of squeezing at the output facet of the laser. A comparison of the data to theoretical predictions suggests that the excess noise measured under free-running conditions could be a result of incomplete side-mode suppression in combination with asymmetrical cross-mode nonlinear gain saturation.
We demonstrate the ability to control quantum coherent Rabi-oscillations in a room-temperature quantum dot semiconductor optical amplifier (SOA) by shaping the light pulses that trigger them. The experiments described here show that when the excitation is resonant with the short wavelength slope of the SOA gain spectrum, a linear frequency chirp affects its ability to trigger Rabi-oscillations within the SOA: A negative chirp inhibits Rabi-oscillations whereas a positive chirp can enhance them, relative to the interaction of a transform limited pulse. The experiments are confirmed by a numerical calculation that models the propagation of the experimentally shaped pulses through the SOA.
This thesis describes the phase and amplitude noise properties of semiconductor lasers subjected to weak, dispersive optical feedback. In the first half, experiments demonstrating reductions in the laser frequency noise power spectrum and spectral linewidth by several orders of magnitude are presented. Weak optical feedback is applied to the laser by an external cavity containing an atomic vapor. The presence of the vapor adds to the dispersion of the cavity and simultaneously locks the laser to a fixed frequency reference. The role of 1/f frequency noise in limiting the effectiveness of this linewidth reduction technique is investigated and 1/f noise is found to be the dominant contribution to the linewidth under strong optical feedback conditions. An electronic feedback scheme utilizing FM sideband locking is then implemented alongside the optical feedback, and an additional reduction in the low frequency 1/f frequency noise power spectrum by over two orders of magnitude is obtained. With both systems operating simultaneously, the spectral linewidth is narrowed from its free-running value of about 20 MHz to 1.4 kHz. Excellent absolute frequency stability is also achieved. In the second half, the effects of optical feedback on the quantum mechanical amplitude noise properties of the laser are examined. A fully quantum mechanical theory of amplitude and phase noise for a semiconductor laser with weak optical feedback is developed, and the nature and limits of the noise reduction using this technique are established. Particular attention is given to the feedback-induced enhancement of the amplitude squeezing which can be obtained in a pump-suppressed semiconductor laser: an improvement in the squeezing by 3 dB is predicted under moderate pumping. Somewhat larger noise reductions are expected when the laser is operating closer to threshold. Measurements performed on a laser biased close to threshold are then described and a reduction in the low frequency amplitude noise power spectrum by 7 dB is obtained. An experimental investigation of the effects of optical feedback on the amplitude squeezing in a semiconductor laser is then discussed. The low frequency squeezing in a room temperature device is increased from 3% below the standard quantum limit (SQL) under free-running conditions to 19% below the SQL with optimal feedback. The experimental results are found to agree poorly with the single-mode model and a multi-mode model including the effects of asymmetrical cross-mode non-linear gain is developed to explain the discrepancy. Finally, further experimental investigation into the generation of amplitude squeezed light is presented using a commercial laser with no intentional external modifications. Squeezing as large as 29% below the SQL is measured using a balanced homodyne detector with the laser operating near room temperature, corresponding to 41% below the SQL at the output facet of the laser.
The nature of phase noise in quantum optics is analyzed. In an experiment involving the measurement of the electromagnetic field the two quantities of interest are the energy and phase of the field. However, measurements of the quantities produce quantum fluctuations. The quantum fluctuations are regarded as noise in the treatment presented here. The quantum system is represented by a probability distribution, the Wigner function, and the quantum fluctuations are treated as stochastic noise associated with the quantity being measured. The difficulties of associating a quantum operator with the phase of the system are reviewed and the related energy-phase uncertainty relation is discussed. The alternate interpretation of the phase noise of a quantum system as being the classical phase noise of the Wigner function is presented. In particular the energy and phase noise of the vacuum state, the coherent state, the squeezed state and the squeezed vacuum are discussed in this way. The squeezed states of light are minimum uncertainty states with respect to the quadrature operators and exhibit noise of one quadrature below the noise level associated with the vacuum. The reduced noise level in one quadrature of the field underlies the importance of squeezed states in many practical applications where there is a need to reduce the quantum noise of one quadrature of coherent light. The periodic phase operator eliminates the difficulties associated with the multivalued nature of phase. The analysis of the vacuum and intense coherent state of Carruthers and Nieto by employing periodic phase operators is reviewed, particularly with respect to the energy-phase uncertainty relations and we generalize the approach to develop a phase operator analysis of the squeezed state in the intense field and vacuum limits. We demonstrate here for the first time that the phase operator is simply related to the phase of the squeezed state in the intense field limit and that the squeezed state is approximately an energy-phase minimum uncertainty state in the low-squeezing limit. Also we enlarge on previous work to demonstrate that the phase operator corresponds simply and unambiguously to the phase of the squeeze parameter for the strongly squeezed vacuum and the intensely squeezed vacuum is an energy-phase minimum uncertainty state for some values of phase. The occurrence of squeezing for the case of two coupled quantum oscillators is presented. The system consisting of one mode of the electromagnetic field coupled to a spinless nonrelativistic electron subjected to an harmonic potential is represented by two coupled harmonic oscillators. The dynamics are compared for the case that the rotating wave approximation is employed and for the case that the counter-rotating terms are included. These calculations have not been performed before. The parametric amplifier Hamiltonian with a nonresonant coupling is also studied in order to provide insight into the effects of the counter-rotating terms. Squeezing of the field produced by the electron is a consequence of the inclusion of the counter-rotating terms. The case of a spinless nonrelativistic electron subject to an harmonic potential and coupled to a continuum of electromagnetic field modes is also considered. The case of two coupled oscillators discussed above is generalized by replacing the oscillator which represents the single-mode field by a bath of oscillators. The effects of including counter-rotating terms and of ignoring the counter - rotating terms in the Hamiltonian are compared. The interaction is assumed to produce a frequency shift and an exponential damping term for the oscillating electron. The frequency shift is assumed to be small in either case and so the Wigner-Weisskopff approximation is employed to solve the equations of motion. We demonstrate the new results that dissipation-induced phase-dependent noise is a consequence of including the counter-rotating terms and that the noise is phase-independent for the case that the counterrotating terms are excluded. The relation between these results and recent work on quantum tunnelling in superconducting quantum interference devices is discussed. We conclude by suggesting further research related to the work in this thesis.
Recent studies have extensively explored chaotic dynamics in quantum optical systems through the mean-field approximation, which corresponds to an ideal, fluctuation-free scenario. However, the inherent sensitivity of chaos to initial conditions implies that even minute fluctuations can be amplified, thereby questioning the applicability of this approximation. Here, we analyze these chaotic effects using stochastic Langevin equations or the Lindblad master equation. For systems operating at frequencies of 10510^5105 to 10710^7107 Hz, we demonstrate that room-temperature thermal fluctuations are sufficient to suppress chaos at the level of expectation values, even under weak nonlinearity. Furthermore, nonlinearity induces deviations from Gaussian phase-space distributions of the quantum state, revealing attractor-like features in the Wigner function. With increasing nonlinearity, the noise threshold for chaos suppression decreases, approaching the scale of vacuum fluctuations. These results provide a bidirectional validation of the quantum mechanical suppression of chaos.