Spin cooling via incoherent feedback in an ensemble of cold 87Rb atoms

Summary form only given. We report an experimental study of a new technique for spin cooling an ensemble of ultracold atoms via quantum non-demolition (QND) measurement and incoherent feedback. This is a form of entropic cooling of the spins that increases the phase space density, in contrast to coherent feedback schemes such as described in Refs.[1, 2]. Our technique has potential applications in quantum optics such as quantum simulations and generation of new quantum states [3,4].We work with ensemble of up to 1.2 x 106 laser cooled 87Rb atoms in the f = 1 ground state, held in a weakly focused (48μm beam waist) single beam optical dipole trap, as described in detail in Ref [5]. We probe the atoms with μs pulses of linear polarized light which are 700 MHz detuned from f = 1 to f´ = 0 D2 transition of 87Rb. We use the output of the (QND) measurement to generate an optical pumping feedback pulse of light with circular polarization and detuning of 80 MHz to the red of the f = 0 f´ = 1 transition. The number of photons in the feedback pulses are controlled with the gain g and are chosen to set the population of Fz to zero. We repeat this sequence on all three collective spin components Fi by applying a magnetic field |B|(1,1,1) and stroboscopically probing at three times the Larmor precession frequency. The effect of the feedback can be described using the effective Hamiltonian τHeff = κ1SzFz where τ is the duration of the pulse, κ1 is a coupling constant and Si is the collective Stokes operator. The measurement output from this interaction is Sout y = Siny + κ1SxFin z which is used to apply feedback to Fz angular momentum component, FFeedback z = Fin z + gSout y . There is a trade-off between the noise of the measurement and the gain of the feedback g which lead to the optimum gain of feedback gopt = - κ1Sxvar(F(0) z ) y ). A generalized model accounting for κ2 1 S2 xvar(F(0) z )+var(S(0) succ- ssive measurement & feedback applied to all three collective spin components shows good agreement with preliminary experimental data (theory curve in Fig.1(c)).