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Nature Communications

Acceleration-induced spectral beats in strongly driven harmonic oscillators

Alexander Sergeevich Kuznetsov, K. Biermann, Paulo Ventura Santos

Published Jul 3, 2024• 3 citations
Publisher

Abstract

The harmonic modulation of coherent systems gives rise to a wealth of physical phenomena, e.g., the AC-Stark effect and Mollow triplets, with important implications for coherent control and frequency conversion. Here, we demonstrate a novel regime of temporal coherence in oscillators harmonically driven at extreme energy modulation amplitudes relative to the modulation quantum. The studies were carried out by modulating a confined exciton-polariton Bose-Einstein condensate (BEC) by an acoustic wave. Features of the new regime are the appearance, in the spectral domain, of a comb of resonances termed acceleration beats with energy spacing tunable by the modulation amplitude and, in the time domain, of temporal correlations at time scales much shorter than the acoustic period, which also depend on the modulation amplitude. These features are quantitatively accounted for by a theoretical framework, which associates the beats with accelerated energy-change rates during the harmonic cycle. These observations are underpinned by the high sensitivity of the BEC energy to the acoustic driving, which simultaneously preserves the BEC's temporal coherence. The acceleration beats are a general feature associated with accelerated energy changes: analogous features are thus also expected to appear under highly accelerated motion e.g., in connection with Cherenkov and Hawking radiation.

DOI
10.1038/s41467-024-49610-5

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The harmonic modulation of coherent systems gives rise to a wealth of physical phenomena, e.g., the AC-Stark effect and Mollow triplets, with important implications for coherent control and frequency conversion. Here, we demonstrate a novel regime of temporal coherence in oscillators harmonically driven at extreme energy modulation amplitudes relative to the modulation quantum. The studies were carried out by modulating a confined exciton-polariton Bose-Einstein condensate (BEC) by an acoustic wave. Features of the new regime are the appearance, in the spectral domain, of a comb of resonances termed acceleration beats with energy spacing tunable by the modulation amplitude and, in the time domain, of temporal correlations at time scales much shorter than the acoustic period, which also depend on the modulation amplitude. These features are quantitatively accounted for by a theoretical framework, which associates the beats with accelerated energy-change rates during the harmonic cycle. These observations are underpinned by the high sensitivity of the BEC energy to the acoustic driving, which simultaneously preserves the BEC's temporal coherence. The acceleration beats are a general feature associated with accelerated energy changes: analogous features are thus also expected to appear under highly accelerated motion e.g., in connection with Cherenkov and Hawking radiation.
The on-demand selective population transfer between states in multilevel quantum systems is a challenging problem with implications for a wide-range of physical platforms including photon and exciton-polariton Bose- Einstein condensates (BECs). Here, we introduce an universal strategy for this selective transfer based on a strong time-periodic energy modulation, which is experimentally demonstrated by using a GHz acoustic wave to control the gain and loss of confined modes of an exciton-polariton BEC in a microcavity. The harmonic acoustic field shifts the energy of the excitonic BEC component relative to the photonic ones, which generates a dynamic population transfer within a multimode BEC that can be controlled by the acoustic amplitude. In this way, the full BEC population can be selectively transferred to the ground state to yield a single-level emission consisting of a spectral frequency comb with GHz repetition rates as well as picosecond-scale correlations. A theoretical model reproduces the observed time evolution and reveals a dynamical interplay between bosonic stimulation and the adiabatic Landau-Zener-like population transfer. Our approach provides a new avenue for the Floquet engineering of light-matter systems and enables tunable single- or multi-wavelength ultrafast pulsed laser-like emission for novel information technologies.
Time-dependent spatial modulation of a quantum condensate plays a key role in the investigation of the dynamics of collective coherent systems. Cold-atom condensates were already manipulated into forming solitons, vortices and optical lattices via the dynamic Stark effect. In the solid-state framework, semiconductor microcavity exciton-polaritons present an excellent platform for observing nonequilibrium condensate dynamics. Furthermore, the dynamic manipulation of exciton-polariton condensates offers numerous potential implementations in all-optical logic devices. We report the first observation of the energy modulation of an exciton-polariton condensate via the dynamic Stark effect. A Stark pulse is employed to induce a transient, coherence-preserving blueshift in the energy of the condensate of femtosecond-scale duration. A novel approach is presented for discerning the Stark effect in a condensate from the uncondensed case according to distinctive features in differential reflectance spectra, including spectro-temporal oscillations enabling to detect the buildup of coherence. The ultrafast and non-invasive modulation of the exciton-polariton condensate demonstrated here opens new research avenues of nonequilibrium physics of solid-state condensates as well as opportunities for polariton-based elements in both classical and quantum information technologies.
We experimentally observe harmonic oscillations in a bosonic condensate of exciton-polaritons confined within an elliptical trap. These oscillations arise from quantum beats between two size-quantized states of the condensate, split in energy due to the trap’s ellipticity. By precisely targeting specific spots inside the trap with nonresonant laser pulses, we control frequency, amplitude, and phase of these quantum beats. The condensate wave function dynamics is visualized on a streak camera and mapped to the Bloch sphere, demonstrating Hadamard and Pauli-Z operations. We conclude that a qubit based on a superposition of these two polariton states would exhibit a coherence time exceeding the lifetime of an individual exciton-polariton by at least two orders of magnitude.
A hydrodynamical version of the time-dependent Gross-Pitaevskii equation has been formulated and applied to the description of a Bose-Einstein condensate (BEC) of 87{}^{87}87Rb atoms in the JILA time-averaged orbiting potential (TOP) trap. The response of the BEC to time-dependent modulations of the trap potential is computed and the characteristic frequencies of a BEC oscillation agree well with those observed in recent experiments. For the axially symmetric m=0m=0m=0 mode of the TOP trap, we find a weak dependence of the oscillatory frequency on the strength of the driving amplitude under conditions comparable to those of current experiments. The free ringing of the BEC that is induced by a transient change in the potential is found to be periodic, in agreement with the predictions of Thomas-Fermi theory. We analyze the harmonic content of the spectral response and consider possibilities for high-harmonic generation in the context of nonlinear atom optics.
In trapped Bose-Einstein condensates, interaction quenches which are abrupt changes of the interaction strength typically implemented via Feshbach tuning, are a practical and widely used protocol to address far-from-equilibrium collective modes. Using both numerical Gross Pitaevskii and analytical schemes we study these interaction-quench-induced collective modes in a harmonically trapped two-dimensional Bose--Einstein condensate contrasting the behavior found at low and high energies. In the low-lying regime, we characterize realistic circumstances in which there is a breakdown of the expected scale invariance so that the collective excitations follow hydrodynamic theory instead of the predictions given by SO(2,1) conformal symmetry. In the high energy regime, we focus on important trap effects associated with acoustic oscillations which have been of interest experimentally. This comprehensive analysis of the collective excitations in trapped two-dimensional Bose-Einstein condensates is experimentally accessible. Through their frequencies and damping, this reflects an important built-in spectroscopy of such many-body states.
In BECs, collisions between condensate atoms give rise to a nonlinear contribution to the dynamics which is typically included as a mean-field term in the Schrodinger equation. This nonlinearity leads to a modification of well-known effects associated with matter waves in periodic potentials and adds a number of phenomena that are absent in the linear problem. We focused on the dynamics of a BEC in an accelerated optical lattice. In the linear case, this gives rise to Bloch oscillations and, above a critical acceleration, to Landau-Zener tunneling. In the nonlinear case, the probability for Landau-Zener tunneling is modified depending on the direction in which it occurs between two bands. By varying the acceleration of the optical lattice and measuring the time-dependence of the interference contrast, we were able to identify the instability regime and the characteristic time in which the dynamical instability destroys the interference pattern. Furthermore, we observed an increase in the condensate dimensions perpendicular to the lattice direction when the unstable region was reached. This indicates a mechanism whereby the longitudinal instability leads to an increase in the transverse release energy