Enhancing laser sideband cooling in one-dimensional optical lattices via the dipole interaction Rebecca N. Palmer ∗ and Almut Beige The School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, United Kingdom (Dated: November 8, 2018) We study resolved sideband laser cooling of a one-dimensional optical lattice with one atom per site, and in particular the effect of the dipole interaction between radiating atoms. For simplicity, we consider the case where only a single cooling laser is applied. We derive a master equation, and solve it in the limit of a deep lattice and weak laser driving. We find that the dipole interaction significantly changes the final temperature of the particles, increasing it for some phonon wavevectors and decreasing it for others. The total phonon energy over all modes is typically higher than in the non-interacting case, but can be made lower by the right choice of parameters. PACS numbers: 37.10.De,37.10.Jk Over the recent decades, a variety of laser cooling tech- niques have been developed [1–4] and implemented [5–9] for cooling trapped atoms or ions to very low tempera- tures. The resulting ultracold atoms can be made into a Bose-Einstein condensate [5, 6]. They can also be put into an optical lattice (an optical standing wave forming a periodic potential [10–12]), where they can be used for quantum simulation of condensed matter systems [12], or potentially for quantum information processing [10]. However, laser cooling does have limitations, which often require it to be followed by the loss of ∼ 99 − 99 . 9% of the atoms by evaporative cooling [5, 6]. We here consider resolved sideband cooling [1, 4], which is mostly used on ions [13] but has been applied to atoms in an optical lattice [14, 15]. This cooling tech- nique works on strongly confined particles: the trapping frequency ν needs to be large compared to the sponta- neous decay rate Γ of the internally excited state. This allows the quantized motional states (with spacing $_{ℏ}$ν ) to be individually resolved. We can hence tune the driv- ing laser to drive mainly a transition to the next lower motional level (Fig. 1), removing one motional quantum per cooling cycle. Equilibrium is reached when this cooling is balanced by heating. For a single particle, heating can occur ei- ther by off-resonant excitation or by the random recoil of spontaneous emission [1]. As confined particles can only be heated in whole quanta $_{ℏ}$ν , heating is rare if $_{ℏ}$ν is large compared to the widths of these heating pro- cesses, $_{ℏ}$Γ and E$_{R}$ ≡ ℏ $^{2}$k2 $_{0}$/ 2 m respectively (here k$_{0}$ is the transition wavenumber and m is the atomic mass). This gives an equilibrium temperature of ∼ $_{ℏ}$Γ $^{2}$/ν , compared to ∼ $_{ℏ}$Γ for free space Doppler cooling [1]. Resolved sideband cooling also requires only one laser frequency, rather than the spread of frequencies required for narrow- line ($_{ℏ}$Γ < E$_{R}$ ) Doppler cooling [2]. When laser cooling is applied to many closely spaced particles, the spontaneous decay rate is modified by in- terference between the emission from different particles, which is called superradiance [16–18]. It is also possible for a photon emitted by one atom to be reabsorbed by another [19]. These two effects together are the dipole- dipole interaction we consider. This interaction exists $^{∗}$Electronic address: R.Palmer@leeds.ac.uk FIG. 1: Energy level diagram of our system. In the left site we show the conventional sideband cooling cycle: for red detun- ing Δ ≈ ν , the resonant excitation process is to the level with one fewer phonons (motional quanta), while in a deep lattice the dominant spontaneous decay process does not change the phonon number. On the right, we show an example of dipole- dipole interaction: the photon emitted by the middle atom is reabsorbed by the right-hand one, moving the excitation from the middle to the right-hand site. In this example the phonon states of both atoms are unchanged, but we will see later that this is not always the case. I. INTRODUCTION arXiv:1001.2493v1 [cond-mat.quant-gas] 14 Jan 2010 |0〉 |1〉 n-1 n n-1 n d-d int. C( r ) laser Ω decay Γ Δ ν ω$_{0}$ a