## Coherent all-optical control of ultracold atoms arrays in permanent magnetic traps |

Optics Express, Vol. 22, Issue 3, pp. 3501-3513 (2014)

http://dx.doi.org/10.1364/OE.22.003501

Acrobat PDF (2296 KB)

### Abstract

We propose a hybrid architecture for quantum information processing based on magnetically trapped ultracold atoms coupled via optical fields. The ultracold atoms, which can be either Bose-Einstein condensates or ensembles, are trapped in permanent magnetic traps and are placed in microcavities, connected by silica based waveguides on an atom chip structure. At each trapping center, the ultracold atoms form spin coherent states, serving as a quantum memory. An all-optical scheme is used to initialize, measure and perform a universal set of quantum gates on the single and two spin-coherent states where entanglement can be generated addressably between spatially separated trapped ultracold atoms. This allows for universal quantum operations on the spin coherent state quantum memories. We give detailed derivations of the composite cavity system mediated by a silica waveguide as well as the control scheme. Estimates for the necessary experimental conditions for a working hybrid device are given.

© 2014 Optical Society of America

## 1. Introduction

1. M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. **T137**, 014001 (2009). [CrossRef]

2. G. Wilpers, P. See, P. Gill, and A. Sinclair, “A monolithic array of three-dimensional ion traps fabricated with conventional semiconductor technology,” Nat. Nanotechnol. **7**, 572–576 (2012). [CrossRef] [PubMed]

3. F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose-Einstein condensate,” Nature **450**, 268–271 (2007). [CrossRef] [PubMed]

6. S. Ritter, C. Nölleke, C. Hahn, A. Reiserer, A. Neuzner, M. Uphoff, M. Mücke, E. Figueroa, J. Bochmann, and G. Rempe, “An elementary quantum network of single atoms in optical cavities,” Nature **484**, 195–200 (2012). [CrossRef] [PubMed]

4. J. Ye, D. Vernooy, and H. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. **83**, 4987–4990 (1999). [CrossRef]

7. P. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature **404**, 365–368 (2000). [CrossRef] [PubMed]

8. M. Kohnen, M. Succo, P. Petrov, R. Nyman, M. Trupke, and E. Hinds, “An array of integrated atom-photon junctions,” Nat. Photonics **5**, 35–38 (2011). [CrossRef]

1. M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. **T137**, 014001 (2009). [CrossRef]

9. A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. Girvin, and R. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature **431**, 162–167 (2004). [CrossRef] [PubMed]

11. C. Eichler, C. Lang, J. Fink, J. Govenius, S. Filipp, and A. Wallraff, “Observation of entanglement between itinerant microwave photons and a superconducting qubit,” Phys. Rev. Lett. **109**, 240501 (2012). [CrossRef]

3. F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose-Einstein condensate,” Nature **450**, 268–271 (2007). [CrossRef] [PubMed]

12. Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature **450**, 272–276 (2007). [CrossRef] [PubMed]

13. P. Treutlein, T. Steinmetz, Y. Colombe, B. Lev, P. Hommelhoff, J. Reichel, M. Greiner, O. Mandel, A. Widera, T. Rom, I. Bloch, and T. Hänsch, “Quantum information processing optical lattices and magnetic microtraps,” Fortschr. Phys. **54**, 702 (2006). [CrossRef]

14. P. Böhi, M. Riedel, J. Hoffrogge, J. Reichel, T. Haensch, and P. Treutlein, “Coherent manipulation of Bose-Einstein condensates with state-dependent microwave potentials on an atom chip,” Nat. Phys. **5**, 592–597 (2009). [CrossRef]

15. M. Riedel, P. Böhi, Y. Li, T. Hänsch, A. Sinatra, and P. Treutlein, “Atom-chip-based generation of entanglement for quantum metrology,” Nature **464**, 1170–1173 (2010). [CrossRef] [PubMed]

16. A. Sørensen, L. Duan, J. Cirac, and P. Zoller, “Many-particle entanglement with Bose-Einstein condensates,” Nature **409**, 63–66 (2000). [CrossRef]

17. T. Byrnes, K. Wen, and Y. Yamamoto, “Macroscopic quantum computation using
Bose-Einstein condensates,” Phys. Rev.
A **85**, 040306 (2012). [CrossRef]

17. T. Byrnes, K. Wen, and Y. Yamamoto, “Macroscopic quantum computation using
Bose-Einstein condensates,” Phys. Rev.
A **85**, 040306 (2012). [CrossRef]

*S*,

^{x}*S*and

^{z}*S*, where

^{z}S^{z}*S*denotes the collective spin operators. Entanglement between two atomic ensembles have been realized in the form of two-mode squeezing such as in the experiments of Polzik and co-workers [18

^{x,z}18. B. Julsgaard, A. Kozhekin, and E. Polzik, “Experimental long-lived entanglement of two macroscopic objects,” Nature **413**, 400–403 (2001). [CrossRef] [PubMed]

19. M. Lettner, M. Mücke, S. Riedl, C. Vo, C. Hahn, S. Baur, J. Bochmann, S. Ritter, S. Dürr, and G. Rempe, “Remote entanglement between a single atom and a Bose-Einstein condensate,” Phys. Rev. Lett. **106**, 210503 (2011). [CrossRef] [PubMed]

8. M. Kohnen, M. Succo, P. Petrov, R. Nyman, M. Trupke, and E. Hinds, “An array of integrated atom-photon junctions,” Nat. Photonics **5**, 35–38 (2011). [CrossRef]

## 2. Proposed device and spin coherent state quantum computation

*N*∼ 1000) of cold atoms to be confined. The atoms may either be an ensemble of cold atoms or a BEC, which may be achieved by standard methods such as laser and evaporative cooling. We use the framework described in [17

17. T. Byrnes, K. Wen, and Y. Yamamoto, “Macroscopic quantum computation using
Bose-Einstein condensates,” Phys. Rev.
A **85**, 040306 (2012). [CrossRef]

*a*and

*b*are the bosonic operators associated with the logical qubit states,

*N*is the number of atoms in the BEC, and

*α*,

*β*are arbitrary coefficients such that |

*α*|

^{2}+ |

*β*|

^{2}= 1. In the following, we asume the logical states are the hyperfine states |

*F*= 1,

*m*= −1〉 and |

_{F}*F*= 2,

*m*= 1〉 of the

_{F}^{87}Rb atoms, respectively [17

**85**, 040306 (2012). [CrossRef]

20. A. Pyrkov and T. Byrnes, “Entanglement generation in quantum networks of Bose-Einstein condensates,” New J. Phys. **15**093019 (2013). [CrossRef]

**85**, 040306 (2012). [CrossRef]

**85**, 040306 (2012). [CrossRef]

**85**, 040306 (2012). [CrossRef]

*i*index runs over all the atoms in one trapping site. As an entangling gate we propose the operaton

*j*and

*j′*label two distinct trapping centers. To this end, initialization of the SC qubits is required, which can be considered to irreversibly take any state to a known state. We shall consider the irreversible process If in a quantum algorithm a different initial state is required, a simple unitary rotation of Eq. (7) can then in turn prepare any state. Finally, the readout of the state is required, such as the projective measurement with the number state basis as For an ensemble of atoms, the number state basis reads where

*σ*= ↑, ↓ and

_{i}*k*is a label running from 1 to 2

*denoting the spin configuration. Futher details on the use of SC qubits for quantum information processing may be found in Refs. [17*

^{N}**85**, 040306 (2012). [CrossRef]

20. A. Pyrkov and T. Byrnes, “Entanglement generation in quantum networks of Bose-Einstein condensates,” New J. Phys. **15**093019 (2013). [CrossRef]

23. T. Byrnes, “Fractality and macroscopic entanglement in two-component Bose-Einstein condensates,” Phys. Rev. A **88**, 023609 (2013). [CrossRef]

## 3. All-optical control

### 3.1. Single SC qubit control

^{87}Rb is that for a two photon transition where |Δ

*m*| = 2, this necessarily requires a flip of the nuclear spin [24]. However, the optical fields only change the state of the electrons. Specifically, the hyperfine states used as the logical states can be written in terms of the electron angular momentum

_{F}*J*and nulcear angular momentum

*I*

*J*-states, these states remain orthogonal. In order to complete the transition, the natural hyperfine coupling is required to complete the transition.

*a*and

*b*) excite the states

*e*and

*f*. For the D1 line of Rubidium (5P

_{1/2}) these are

*σ*

^{±}transition. The two intermediate states are connected by a transition element determined by the hyperfine interaction. The Hamiltonian where

*g*is the Rabi frequency of the laser transitions, Δ is the energy detuning of the laser transition to the atomic transitions, and

_{a,b}/h̄*A*is the hyperfine coupling. The operators are defined as for the BEC case as

*J*

^{+}=

*e*

^{†}

*a*,

*K*

^{+}=

*f*

^{†}

*b*,

*L*

^{+}=

*e*

^{†}

*f*,

*n*=

^{a}*a*

^{†}

*a*,

*n*=

^{b}*b*

^{†}

*b*,

*n*=

^{e}*e*

^{†}

*e*,

*n*=

^{f}*f*

^{†}

*f*. For the ensemble case these are defined as

*e*,

*f*states creates an effective Hamiltonian where the effective single SC qubit Rabi frequency is The use of excited states necessarily introduces an additional decoherence channel due to spontaneous decay. The effects of spontaneous emission may be modeled by the master equation Figure 2(b) shows the Rabi oscillations induced by the laser configuration starting from an initial state |1, 0〉〉 for the BEC case. The spontaneous emission causes an effective decoherence. The damping envelope of the Rabi oscillations occur at a rate of This gives a condition for experimentally controllable parameters

*g*, Δ to ensure that the damping rate should be at least as long as other decoherence timescales. For the D1 line in

_{a,b}^{87}Rb, the spontaneous emission rate is Γ = 2

*π*× 6MHz, and the hyperfine coupling is

*A/h̄*= 400MHz [25]. Assuming typical parameters

*N*= 10

^{3},

*g*=

_{a}*g*= 100

_{b}*A*, and Δ = 1000

*A*, we obtain Ω

_{1}= 8MHz and Γ

_{eff}= 2

*π*× 60kHz, allowing for many coherent oscillations during the effective decoherence.

*h̄ω*= (

^{z}*E*−

_{a}*E*)/2 and

_{b}*E*are the energy levels of the logical states. For example, for

_{a,b}^{87}Rb atoms the energy difference between the

*F*= 1 and

*F*= 2 levels gives

*ω*/2

^{z}*π*= 3.4GHz.

### 3.2. Initialization and measurement

30. D. Press, T. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature **456**, 218–221 (2008). [CrossRef] [PubMed]

*g*= 0 and the detuning is Δ = 0. By application of only one branch of the Λ system, this forces all states towards the state |0, 1〉〉, since an atom in level

_{b}*a*efficiently transfered to level

*e*via the laser, from which it may decay into level

*b*via spontaneous emission. After decay into level

*b*it is trapped there. In Fig. 2(c) we plot the state from two different initial conditions by evolving (15). We see that in all cases the population evolves towards 〈

*S*〉/

^{z}*N*= −1, corresponding to the state |0, 1〉〉. Measurement is performed by the same process. Spontaneous emission causes an emission of photons due to the decay process between the levels

*f*↔

*b*. Every detected photon arises due to the presence of an atom in level

*a*, thus by counting the number of photons one may obtain a measurement in the

*S*basis of Eq. (9). To obtain expectation values, the total number of atoms is also needed, which would be obtained in an initial calibration step, where initially all the atoms are driven into the level

^{z}*b*. Then by setting

*g*= 0 instead, turning on

_{a}*g*and counting the total number of photons, one obtains the total number of atoms

_{b}*N*.

### 3.3. Two SC qubit entanglement

**85**, 040306 (2012). [CrossRef]

*S*,

^{n}*n*=

*x*,

*y*,

*z*), and any two BEC qubit operation. We now describe how to implement a

20. A. Pyrkov and T. Byrnes, “Entanglement generation in quantum networks of Bose-Einstein condensates,” New J. Phys. **15**093019 (2013). [CrossRef]

*b*and the excited state

_{i}*e*of the atoms. To initiate the entanglement between two nodes

_{i}*i*and

*j*, an off-resonant laser for the transition

*b*↔

_{i}*e*is delivered through the control waveguide, labeled by 3⃞ in Fig. 1(a). Entanglement is generated by the process of photon emission from node

_{i}*i*and absorption by node

*j*, by traveling through the silica waveguide labeled by 6⃞, or vice versa. For nodes without the laser illumination, the photon does not get absorbed since they are off-resonant of the transition to the excited state. The Hamiltonian describing the system is given by where

*p*are the photon annihilation operators for each cavity,

_{i}*G*is the cavity-atom coupling,

*h̄ω*

_{0}is the energy difference between the exited state

*e*and the ground state

_{i}*b*, and

_{i}*h̄ω*is the resonant mode of the cavity. The photons may hop between the cavities through the waveguides, according to the Hamiltonian where

*ν*is the cavity-waveguide hopping amplitude and

*ϕ*is the combined phase picked up due to the length of the waveguide and the presence of adjustable phase shifters [31

_{j}31. J. Matthews, A. Politi, A. Stefanov, and J. OBrien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics **3**, 346–350 (2009). [CrossRef]

37. J. Lepert, M. Trupke, M. Hartmann, M. Plenio, and E. Hinds, “Arrays of waveguide-coupled optical cavities that interact strongly with atoms,” New J. Phys. **13**, 113002 (2011). [CrossRef]

*p*with odd

_{j}*j*label photons within cavities, while even

*j*label photons in waveguides. Assuming that the coupling strengths

*ν*≫

*G*, and a one-dimensional configuration of cavities and waveguides, we may diagonalize the Hamiltonian

*H*

_{c-w}using where

*M*is the total number of cavities, and

*𝒩*is a normalization factor. For this case there is always zero energy mode

_{k}*k*=

*M*which has the same energy as the original cavity resonance. This mode is used as the common mode connecting all the SC qubits to each other, with all other modes being off-resonant and do not contribute to the operation. From here the same derivation as [20

**15**093019 (2013). [CrossRef]

**15**093019 (2013). [CrossRef]

*is the total phase that is picked up by the photon when traveling between nodes*

_{ij}*i*and

*j*. Equation (21) shows that the two qubit interactions can be produced. However, as by product we have also created unwanted effective self-interaction terms

*=*

_{ij}*π*/2, to remove the

*h̄*Ω

_{2}has an odd parity with Δ, we may apply a second interaction but with a reverse detuning −Δ, which removes the unwanted self-interaction terms.

## 4. Experimental design

### 4.1. The permanent magnetic traps

26. M. Singh, M. Volk, A. Akulshin, A. Sidorov, R. McLean, and P. Hannaford, “One dimensional lattice of permanent magnetic microtraps for ultracold atoms on an atom chip,” J. Phys. B At. Mol. Opt. Phys. **41**, 065301 (2008). [CrossRef]

29. A. Abdelrahman, M. Vasiliev, K. Alameh, and P. Hannford, “Asymmetrical two-dimensional magnetic lattices for ultracold atoms,” Phys. Rev. A **82**, 012320 (2010). [CrossRef]

*d*

_{min}in space, as shown in Fig. 1(b). The size of the patterns (square holes of size

*α*in this case) and their separation distance

_{h}*α*determine the value of

_{s}*d*

_{min}according to

29. A. Abdelrahman, M. Vasiliev, K. Alameh, and P. Hannford, “Asymmetrical two-dimensional magnetic lattices for ultracold atoms,” Phys. Rev. A **82**, 012320 (2010). [CrossRef]

*α*= 3

_{h}*μm*and

*α*= 100

_{s}*μm*. The reference magnetic field

*B*

_{ref}is defined as

*B*

_{ref}=

*B*

_{0}(1 −

*e*

^{−}

*) where*

^{βτ}*τ*is the thin film thickness,

*M*is the thin film magnetization along the z-axis, and

_{z}*β*=

*π/α*. Due to their spherical quadruple nature, these particular types of magnetic traps produce zero magnetic field minimum where to elevate the minimum value of the trapping magnetic field away from zero external magnetic bias fields are often used, hence avoiding the Majorana spin flip.

29. A. Abdelrahman, M. Vasiliev, K. Alameh, and P. Hannford, “Asymmetrical two-dimensional magnetic lattices for ultracold atoms,” Phys. Rev. A **82**, 012320 (2010). [CrossRef]

*x*-axis by applying a bias field along the

*x*-axis of

*B*

_{x}_{-bias}= −1G. A vertical displacement is simulated in Fig. 3(b) according to the application of external field along the

*z*-axis of magnitude

*B*

_{z}_{-bias}= −1G.

### 4.2. Atoms-optical fields strong coupling

32. M. Malak, N. Gaber, F. Marty, N. Pavy, E. Richalot, and T. Bourouina, “Analysis of Fabry-Pérot optical micro-cavities based on coating-free all-Silicon cylindrical Bragg reflectors,” Opt. Express **21**, 2378–2392 (2013). [CrossRef] [PubMed]

34. M. Malak, F. Marty, N. Pavy, Y. Peter, A. Liu, and T. Bourouina, “Micromachined Fabry-Perot resonator combining submillimeter cavity length and high quality factor,” Appl. Phys. Lett. **98**(21), 211113 (2011). [CrossRef]

8. M. Kohnen, M. Succo, P. Petrov, R. Nyman, M. Trupke, and E. Hinds, “An array of integrated atom-photon junctions,” Nat. Photonics **5**, 35–38 (2011). [CrossRef]

35. S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A **77**, 109–111 (2003). [CrossRef]

36. G. Lepert, M. Trupke, E. Hinds, H. Rogers, J. Gates, and P. Smith, “Demonstration of UV-written waveguides, Bragg gratings and cavities at 780 nm, and an original experimental measurement of group delay,” Opt. Express **19**, 24933–24943 (2011). [CrossRef]

32. M. Malak, N. Gaber, F. Marty, N. Pavy, E. Richalot, and T. Bourouina, “Analysis of Fabry-Pérot optical micro-cavities based on coating-free all-Silicon cylindrical Bragg reflectors,” Opt. Express **21**, 2378–2392 (2013). [CrossRef] [PubMed]

34. M. Malak, F. Marty, N. Pavy, Y. Peter, A. Liu, and T. Bourouina, “Micromachined Fabry-Perot resonator combining submillimeter cavity length and high quality factor,” Appl. Phys. Lett. **98**(21), 211113 (2011). [CrossRef]

*i*= 1, 2 labeling the two cavities. The inner mirrors have an associated reflection coefficient of

*L*and has a phase

^{w}*ϕ*. Here

^{w}*R*is the reflectivity. The reflected optical fields from the first microcavity, the silica waveguide resonator and the second optical microcavity are written, respectively, as We use these ratios to define the reflection coefficients

_{i}37. J. Lepert, M. Trupke, M. Hartmann, M. Plenio, and E. Hinds, “Arrays of waveguide-coupled optical cavities that interact strongly with atoms,” New J. Phys. **13**, 113002 (2011). [CrossRef]

*L*(

^{w}*μm*), we find that the resonance frequency for the two individual cavities is

*c*the speed of light (Fig. 5 shows the simulation of the composite cavity, as detailed below), assuming parameters for the D2 line of

^{87}Rb. For the whole composite system the resonance frequency is

*ω*= 2

_{res}*π*× 0.0021GHz. With a beam waist of roughly (2–4

*μm*) we determine the cavity Bragg mirror radius of curvatures such that with

*ω*

_{0}chosen to be 4

*μm*(the diameter of the silica waveguide).

*N*atoms and the composite cavity-waveguide system to be which is of the order of

*g*is much greater than the decay rate

^{cw}*κ*= 2

*π*× 6MHz, for

^{87}Rb. The amplitude decay rate

*γ*for the cavity and the waveguide are calculated independently such that

_{c/w}*t*is the time of the photon round trip

_{i}*i*is the cavity and the waveguide index. For a cavity of length 40

*μm*with

*γ*

_{c}_{1}∼ 2

*π*× 0.028GHz which we will also consider to be equal to the decay rate

*γ*

_{c}_{2}of the second cavity. For the silica waveguide of optical length

*n*(

_{si}L^{w}*n*is the fused silica refractive index) we calculate the decay rate with

_{si}*L*= 100

^{w}*μm*such that

*γ*∼ 2

_{w}*π*× 0.0077GHz. Fig. 5 shows the reflected intensity of a composite cavity system (two micro-cavities mediated by a single silica waveguide). The simulation input parameters are

*L*= 4mm. Both cavities are at resonance and dips are symmetrically distributed around the zero-resonance with first two dips at the normal modes of the composite cavity system [37

^{w}37. J. Lepert, M. Trupke, M. Hartmann, M. Plenio, and E. Hinds, “Arrays of waveguide-coupled optical cavities that interact strongly with atoms,” New J. Phys. **13**, 113002 (2011). [CrossRef]

## 5. Summary and conclusions

6. S. Ritter, C. Nölleke, C. Hahn, A. Reiserer, A. Neuzner, M. Uphoff, M. Mücke, E. Figueroa, J. Bochmann, and G. Rempe, “An elementary quantum network of single atoms in optical cavities,” Nature **484**, 195–200 (2012). [CrossRef] [PubMed]

## Acknowledgments

## References and links

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28. | S. Whitlock, R. Gerritsma, T. Fernholz, and R. Spreeuw, “Two-dimensional array of microtraps with atomic shift register on a chip,” New J. Phys. |

29. | A. Abdelrahman, M. Vasiliev, K. Alameh, and P. Hannford, “Asymmetrical two-dimensional magnetic lattices for ultracold atoms,” Phys. Rev. A |

30. | D. Press, T. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature |

31. | J. Matthews, A. Politi, A. Stefanov, and J. OBrien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics |

32. | M. Malak, N. Gaber, F. Marty, N. Pavy, E. Richalot, and T. Bourouina, “Analysis of Fabry-Pérot optical micro-cavities based on coating-free all-Silicon cylindrical Bragg reflectors,” Opt. Express |

33. | M. Malak, F. Marty, N. Pavy, Y. Peter, A. Liu, and T. Bourouina, “Cylindrical surfaces enable wavelength-selective extinction and sub-0.2 nm linewidth in 250μm-gap silicon Fabry-Perot cavities,” J. Microelectromech. Syst. |

34. | M. Malak, F. Marty, N. Pavy, Y. Peter, A. Liu, and T. Bourouina, “Micromachined Fabry-Perot resonator combining submillimeter cavity length and high quality factor,” Appl. Phys. Lett. |

35. | S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A |

36. | G. Lepert, M. Trupke, E. Hinds, H. Rogers, J. Gates, and P. Smith, “Demonstration of UV-written waveguides, Bragg gratings and cavities at 780 nm, and an original experimental measurement of group delay,” Opt. Express |

37. | J. Lepert, M. Trupke, M. Hartmann, M. Plenio, and E. Hinds, “Arrays of waveguide-coupled optical cavities that interact strongly with atoms,” New J. Phys. |

38. | M. Hijlkema, B. Weber, H. Specht, S. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature |

**OCIS Codes**

(020.1475) Atomic and molecular physics : Bose-Einstein condensates

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: October 17, 2013

Revised Manuscript: December 9, 2013

Manuscript Accepted: December 10, 2013

Published: February 6, 2014

**Citation**

Ahmed Abdelrahman, Tetsuya Mukai, Hartmut Häffner, and Tim Byrnes, "Coherent all-optical control of ultracold atoms arrays in permanent magnetic traps," Opt. Express **22**, 3501-3513 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-3501

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