# Single Atoms Preparation Using Light-Assisted Collisions

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## Abstract

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## 1. Introduction

## 2. Light-Assisted Collisions Between Two Atoms

**Figure 1.**Light assisted collisions model: interaction potentials as a function of internuclear separation R. Red arrows represent the process of excitation of two ground state atoms to an attractive potential (red curve). Blue arrows represent the process of excitation of the atoms to a repulsive potential (blue curve). Figure adapted from [44].

**Figure 2.**Dressed state picture for a repulsive collisional process showing an avoided crossing at ${R}_{c}$: (

**A**) Possible paths for elastic collisions. Path ER 1 is the case where the atoms undergo adiabatic following both times at ${R}_{c}$. Path ER 2 is the case where the atoms undergo LZ transition both times at ${R}_{c}$. (

**B**) Possible paths for inelastic collisions (IR 1 and IR 2).

**Figure 3.**Dressed state picture for an attractive collisional process showing an avoided crossing at ${R}_{c}$: (

**A**) Possible paths for elastic collisions (EA 1). (

**B**) Possible paths for inelastic collisions (IA 1 and IA 2).

## 3. Experimental Apparatus

**Figure 4.**Schematic of the experimental apparatus. Figure adapted from [35].

## 4. Dynamics of Two Atoms Undergoing Light-Assisted Collisions in a FORT

#### 4.1. Light-Assisted Collisions Between Two Atoms in a FORT

**Figure 5.**Light-assisted collisions between two atoms with laser cooling. Path (a) shows two colliding atoms escaping ($2-0$ loss), leaving no atoms inside the trap. Path (b) shows one of the two colliding atoms escaping ($2-1$ loss), leaving one atom inside the trap. Path (c) shows neither of the two colliding atoms escaping. Laser cooling removes the energy of the atoms.

#### 4.2. Two-Atom Light-Assisted Collisions Induced by Red-Detuned Light

**Figure 6.**The probability densities of the released energy $D\left({E}_{r}\right)$ for head-on collisions induced with light with red detunings of 45, 75 and 105 MHz. The probability of a high energy release are generally small. Figure adapted from [36].

**Figure 7.**Experimental procedure to observe the dynamics of two atoms inside a FORT under the influence of near resonant lights: (II) Verify that there are two atoms in the trap initially by fluorescence imaging. (III) Expose the atoms with near resonant light beams (Six D2 cooling beams and a D1 collision beam) with variable duration $\Delta t$. (IV) Measure the remaining number of atoms.

**Figure 8.**Two-atom evolution when exposed to red-detuned light as a function of $\Delta t$. Light parameters: The collision beam is 45 MHz red-detuned from the $D1$ $F=2$ to ${F}^{\prime}=3$ transition at the centre of the FORT. Figures (

**A**) and (

**B**) have cooling beams intensities of 11 W/m${}^{2}$ and 19 W/m${}^{2}$ respectively. The probabilities of two, one and zero atoms remaining in the trap are indicated by green circles, blue squares and red triangles respectively. The dotted lines are the simulated plots. Error bars represent a statistical confidence of $68.3\%$. Figure adapted from [36].

**Figure 9.**Simulated evolution of individual and the combined energies of the atom pair: (

**A**) is the case of $2-1$ loss and (

**B**) is the case of $2-0$ loss. The dashed lines indicate when inelastic collisions occurred. In between the collisions, the energies of the atoms are lowered due to the laser cooling effect. Figure adapted from [36].

#### 4.3. Two-Atom Light-Assisted Collisions Induced by Blue-Detuned Light

**Figure 10.**Two-atom evolution when exposed to blue-detuned light as a function of $\Delta t$: (

**A**) The collision beam is 85 MHz blue-detuned from the $D1$ $F=2$ to ${F}^{\prime}=3$ transition at the centre of the FORT. (

**B**) Other parameters remained the same but the collision beam is 185 MHz blue-detuned. Green circles, blue squares and red triangles are the probabilities of the experiment ending with two, one and zero atoms respectively. The dotted lines are the simulated plots. Error bars represent a statistical confidence of $68.3\%$. Figure adapted from [44].

## 5. High Efficiency Preparation of Single Atoms Using Repulsive Light-Assisted Collisions

**Figure 11.**Single atom preparation sequence using blue-detuned collision beam and cooling light: (

**1**) Sample preparation stage: about 20 atoms are loaded into the FORT from a compressed Magneto-Optical Trap (CMOT); (

**2**) Isolation stage: a combination of in-trap laser cooling and light-assisted collisions induced by blue-detuned beam are used to make the atoms escape the trap one by one via $2-1$ loss channel. (

**3**) Collisions stop when only one atom is left inside the trap. (

**4**) Imaging stage: measurement of the number of atoms inside the trap by fluorescent imaging. The inset shows an image of one atom. Figure adapted from [30].

**Figure 12.**Histogram of the integrated fluorescence for 3200 realizations, representing $91\%$ single atom loading efficiency (statistical error less than $0.01\%$) [30].

#### 5.1. Dependence on Collision Beam Parameters

**Figure 13.**Probabilities of loading one (blue squares), two (green circles) and zero (red triangles) atom as a function of collision beam detuning Δ (

**left figure**) and collision beam power (

**right figure**). Figure adapted from [30].

#### 5.2. Dependence on Cooling Light Parameters

**Figure 14.**Loading probabilities as a function of cooling beams power (per beam) during the isolation stage. Blue squares, red triangles and green circles are probabilities of loading one, zero and two atoms respectively. The thick pink continuous line is a result of the loading simulation, described in [44]. Figure adapted from [30].

#### 5.3. Limiting Factors

#### 5.4. Loading Single Atom without Blue-Detuned Induced Collision Beam

## 6. Repulsive Light-Assisted Collisions in Collisional Blockade Preparation of Single Atoms

#### 6.1. Collisional Blockade Model

#### 6.2. Efficient Preparation of Single Atom in Collisional Blockade Regime

**Figure 15.**Experimental sequence for efficient preparation of single atom in a tight microtrap where the collisional blockade takes place. Figure adapted from [35].

**Figure 16.**Probability of loading one atom (${p}_{1}$) as a function of loading time with a trap depth of $h\times 47$ MHz. The solid lines are fitted functions with Equation (2) in Section 6.1. Figure adapted from [35].

#### 6.3. Dependence on Trap Depth

**Figure 17.**(

**A**) Probability of loading one atom with 60 ms loading time ${p}_{1}\left(t=60\phantom{\rule{3.33333pt}{0ex}}\mathrm{ms}\right)$ as a function of trap depth. Blue circles represent experimental data taken with the presence of collision beam, while red crosses are those taken without collision beam. The single atom loading efficiency peaks at trap depth around $h\times 47$ MHz. (

**B**) (

**i**) Level diagram for ${}^{85}$Rb atom in free space. (

**ii**) Light-shifted level diagram for ${}^{85}$Rb atom in the centre of the FORT with $h\times 47$ MHz trap depth. Red, purple and blue arrows represent the frequencies of MOT beams, repump beam and the collision beam respectively. Figure adapted from [35].

#### 6.4. Dependence on Blue-Detuned Collision Beam Parameters

**Figure 18.**Probability of loading one atom as a function of power of the collision beam (

**left figure**) and detuning of the collision beam, Δ (

**right figure**). Figure adapted from [35].

## 7. Summary and Future Directions

**Figure 19.**Some examples of works with different atomic species using light-assisted collisions to prepare a single atom in a FORT with known trap waist. The single atom preparation efficiency is quoted as the single trap efficiency. Blue dots represent works that employs repulsive light-assisted collisions. Note: * The works using Cs are conducted in a blue-detuned FORT, so the individual trap size are not directly comparable to the other works that use red-detuned FORT.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References and Notes

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Fung, Y.H.; Sompet, P.; Andersen, M.F.
Single Atoms Preparation Using Light-Assisted Collisions. *Technologies* **2016**, *4*, 4.
https://doi.org/10.3390/technologies4010004

**AMA Style**

Fung YH, Sompet P, Andersen MF.
Single Atoms Preparation Using Light-Assisted Collisions. *Technologies*. 2016; 4(1):4.
https://doi.org/10.3390/technologies4010004

**Chicago/Turabian Style**

Fung, Yin Hsien, Pimonpan Sompet, and Mikkel F. Andersen.
2016. "Single Atoms Preparation Using Light-Assisted Collisions" *Technologies* 4, no. 1: 4.
https://doi.org/10.3390/technologies4010004