Trapping and cooling particles using a moving atom diode and an atomic mirror

We propose a theoretical scheme for atomic cooling, i.e., the compression of both velocity and position distribution of particles in motion. This is achieved by collisions of the particles with a combination of a moving atomic mirror and a moving atom diode. An atom diode is a unidirectional barrier, i.e., an optical device through which an atom can pass in one direction only. We show that the efficiency of the scheme depends on the trajectory of the diode and the mirror. We examine both the classical and quantum mechanical descriptions of the scheme, along with the numerical simulations to show the efficiency in each case.

Figure 1

(a), (b) Diode-mirror setting: a particle approaches the moving diode-mirror system; it can enter one way through the diode in (a) but in (b) from the other direction the diode behaves as another mirror traveling at a different velocity. (c), (d) Motion of the atom diode and the mirror with trajectories (c) $\sim \sqrt{t}$ and (d) $\sim t$.

Figure 2

Classical setting: graph of the velocity of the particle as a function of time; each symbol indicates the velocity of the particle after a collision; parameters for linear scheme (green dots): $v_m=d/T$, $v_d=0.9v_m$; parameters for square root scheme (red triangles): ${\alpha }_m=v_m\sqrt{T}$, ${\alpha }_d=v_d\sqrt{T}$.

Figure 3

Classical setting: plot of $\frac{\left|v_f\right|}{v_0}$ vs initial particle velocity $v_0$ and initial particle position $x_0$: (a) velocity $v_f$ after the last collision with the mirror; (b) velocity $v_f$ after the last collision with the diode. Linear scheme (green, lower planes) and square-root scheme (red, higher planes); other parameters are the same as in Fig. 2.

Figure 4

Classical setting: comparison between velocity distribution using the linear and square-root schemes: initial velocity distribution for both schemes (shifted, black, lowest broad distribution) and final velocity distribution for the square-root scheme, $v_0=10v_m$ (red, thick, solid line) and $v_0=15v_m$ (red, thick, dashed line), and for the linear scheme, $v_0=10v_m$ (green, thin, solid line) and $v_0=15v_m$ (green, thin, dashed line). The dots above the plots correspond to a single-particle simulation with initial velocity $v_0$ and initial position $x_0$; other parameters: $x_0=-0.8d,\mathrm{\Delta }x=0.1d,\mathrm{\Delta }v=5v_m$; other parameters are the same as in Fig. 2.

Figure 5

Classical setting: (a) shifted initial distribution $\rho (0,x,v)$ and (b) final distribution $\rho (T,x,v)$. Both distributions are scaled such that their maximum is one. Linear scheme, $v_0=10v_m$; other parameters as in Fig. 4.

Figure 6

Quantum atom diode and atomic mirror scheme.

Figure 7

Probability distributions: initial distribution (shifted, black, solid lines), final distributions for the classical setting (red, thick line), quantum setting with $v_0=10v_m$ (green, thin line) and quantum setting with $v_0=8v_m$ (blue, dashed line); (a) velocity space, (b) velocity space zoomed in, and (c) position space. Common parameters: $v_d=0.9v_m$, $v_0=10v_m$, $\mathrm{\Delta }v=5v_m$, $x_0=-0.8d$, and $\mathrm{\Delta }x=0.1d$. Additional parameters in the quantum setting: $V_{0,d/m}=5\times {10}^6\hslash /T$, $V_{0,c}=4\times {10}^4\hslash /T$, $v_c=0.98v_m$, ${\sigma }_c=0.0006d,{\sigma }_d={\sigma }_m=0.0001d$, and $m=1000T\hslash /d^2$.

Figure 8

Final quantum velocity distribution with decreasing ${\sigma }_{d/m}$: ${\sigma }_{d/m}=0.0008d$ (blue, thick, solid line), ${\sigma }_{d/m}=0.0004d$ (black, dashed line), ${\sigma }_{d/m}=0.0001d$ (green, thin, solid line), and classical distribution (red, dotted line). $V_{d/m}=5\times {10}^5\hslash /T$; other parameters are the same as in Fig. 7.

Figure 9

Final quantum velocity distribution with different masses: $m=500T\hslash /d^2$ (green, thin, solid line), $m=1000T\hslash /d^2$ (black, dashed line), $m=1500T\hslash /d^2$ (blue, thick, solid line), and $m=2000T\hslash /d^2$ (red, dotted line). $V_{d/m}=5\times {10}^5\hslash /T$ and ${\sigma }_{d/m/c}=0.001d$; other parameters are the same as in Fig. 7.