High harmonic generation from a Bose-Einstein condensate

Abstract

Lasers provide intense coherent radiation, essential to cool and trap atoms into a Bose-Einstein condensate or can alternatively drive the non-linear dynamics of high-order harmonic generation. Yet, these two fundamental processes remained of independent consideration. Here, we connect matter waves at ultracold temperatures with radiation bursts on the ultrafast attosecond timescale. We do this by exploring high harmonic generation from a Bose-Einstein condensate. We show that the quantum state of the generated harmonics of a driven Bose gas is a classical mixture, while below the critical temperature of Bose-Einstein condensation the emitted harmonic radiation is in a pure quantum state. These states furthermore exhibit squeezing and entanglement across all field modes.

Figures (2)

• Figure 1: HHG from a BEC: Driving the process of high-harmonic generation (HHG) in a Bose-Einstein condensate (BEC) give rise to distinct quantum states of the harmonics scattered from the condensate. Above the critical temperature ($T > T_c$) the state is a classical mixture of Gaussian states, while below the critical temperature $(T < T_c)$ the harmonic field is in a pure quantum state, exhibiting entanglement and squeezing.
• Figure 2: Bosonic modes: Schematic representation of the mode structure of the driven Bose gas. The atoms in the internal electronic ground state $\ket{g}$ are trapped in a harmonic oscillator potential with the center of mass modes $\ket{g\vb{n}} \equiv \ket{\vb{n}}$ of energy $E_{\vb{n}}$. Due to the interaction with the short and intense driving pulse, the electronic degree of freedom is excited into a continuum state $\ket{e}$, such that the corresponding atoms are associated to the excited state potential $\ket{e\vb{m}} \equiv \ket{\vb{m}}$ with energy $E_{\vb{m}}'$. The driving field induces transitions from each ground state atom into a wavepacket (orange) of excited state atoms governed by the Franck-Condon like factors $\eta_{\vb{n}\vb{m}}$.