Abstract

Atomic memories for flying photonic qubits are an essential ingredient for many applications like e.g. quantum repeaters. Verification of the coherent transfer of information from a light field to an atomic superposition is usually obtained using an optical read-out. In this paper we report the direct detection of the atomic coherence by means of atom interferometry. We experimentally verified both that a bichromatic laser field closing a Raman transition imprints a distinct, controllable phase on the atomic coherence and that it can be recovered after a variable time delay.

© 2014 Optical Society of America

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  1. H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
    [CrossRef]
  2. H. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
    [CrossRef] [PubMed]
  3. D. P. DiVincenzo, “Quantum computation,” Science 270, 255–261 (1995).
    [CrossRef]
  4. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2010).
    [CrossRef]
  5. A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802 (2002).
    [CrossRef]
  6. M. Eisaman, A. André, F. Massou, M. Fleischhauer, A. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438, 837–841 (2005).
    [CrossRef] [PubMed]
  7. K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nature Phys. 7, 13–16 (2011).
    [CrossRef]
  8. M. Hosseini, G. Campbell, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Unconditional room-temperature quantum memory,” Nature Phys. 7, 794–798 (2011).
    [CrossRef]
  9. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
    [CrossRef] [PubMed]
  10. C.-W. Chou, J. Laurat, H. Deng, K. Choi, H. De Riedmatten, D. Felinto, and H. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
    [CrossRef] [PubMed]
  11. S. L. Christensen, J. B. Béguin, H. L. Sørensen, E. Bookjans, D. Oblak, J. H. Müller, J. Appel, and E. S. Polzik, “Toward quantum state tomography of a single polariton state of an atomic ensemble,” New J. Phys. 15, 015002 (2013).
    [CrossRef]
  12. S. L. Christensen, J. B. Béguin, E. Bookjans, H. L. Sørensen, J. H. Müller, J. Appel, and E. S. Polzik, “Quantum interference of a single spin excitation with a macroscopic atomic ensemble,” arxiv: [quant-ph] 1309.2514v2 (2013).
  13. J. Petrovic, I. Herrera, P. Lombardi, F. Schaefer, and F. S. Cataliotti, “A multi-state interferometer on an atom chip,” New J. Phys. 15, 043002 (2013).
    [CrossRef]
  14. F. Minardi, C. Fort, P. Maddaloni, M. Modugno, and M. Inguscio, “Time-domain atom interferometry across the threshold for Bose-Einstein condensation,” Phys. Rev. Lett. 87, 170401 (2001).
    [CrossRef] [PubMed]
  15. R. J. Cook and B. Shore, “Coherent dynamics of N-level atoms and molecules. III. An analytically soluble periodic case,” Phys. Rev. A 20, 539 (1979).
    [CrossRef]
  16. D. M. Harber, H. J. Lewandowski, J. M. McGuirk, and E. A. Cornell, “Effect of cold collisions on spin coherence and resonance shifts in a magnetically trapped ultracold gas,” Phys. Rev. A 66, 053616 (2002).
    [CrossRef]

2013 (2)

S. L. Christensen, J. B. Béguin, H. L. Sørensen, E. Bookjans, D. Oblak, J. H. Müller, J. Appel, and E. S. Polzik, “Toward quantum state tomography of a single polariton state of an atomic ensemble,” New J. Phys. 15, 015002 (2013).
[CrossRef]

J. Petrovic, I. Herrera, P. Lombardi, F. Schaefer, and F. S. Cataliotti, “A multi-state interferometer on an atom chip,” New J. Phys. 15, 043002 (2013).
[CrossRef]

2011 (2)

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nature Phys. 7, 13–16 (2011).
[CrossRef]

M. Hosseini, G. Campbell, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Unconditional room-temperature quantum memory,” Nature Phys. 7, 794–798 (2011).
[CrossRef]

2008 (1)

H. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[CrossRef] [PubMed]

2007 (1)

C.-W. Chou, J. Laurat, H. Deng, K. Choi, H. De Riedmatten, D. Felinto, and H. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

2005 (1)

M. Eisaman, A. André, F. Massou, M. Fleischhauer, A. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438, 837–841 (2005).
[CrossRef] [PubMed]

2002 (2)

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802 (2002).
[CrossRef]

D. M. Harber, H. J. Lewandowski, J. M. McGuirk, and E. A. Cornell, “Effect of cold collisions on spin coherence and resonance shifts in a magnetically trapped ultracold gas,” Phys. Rev. A 66, 053616 (2002).
[CrossRef]

2001 (2)

F. Minardi, C. Fort, P. Maddaloni, M. Modugno, and M. Inguscio, “Time-domain atom interferometry across the threshold for Bose-Einstein condensation,” Phys. Rev. Lett. 87, 170401 (2001).
[CrossRef] [PubMed]

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

1998 (1)

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[CrossRef]

1995 (1)

D. P. DiVincenzo, “Quantum computation,” Science 270, 255–261 (1995).
[CrossRef]

1979 (1)

R. J. Cook and B. Shore, “Coherent dynamics of N-level atoms and molecules. III. An analytically soluble periodic case,” Phys. Rev. A 20, 539 (1979).
[CrossRef]

André, A.

M. Eisaman, A. André, F. Massou, M. Fleischhauer, A. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438, 837–841 (2005).
[CrossRef] [PubMed]

Appel, J.

S. L. Christensen, J. B. Béguin, H. L. Sørensen, E. Bookjans, D. Oblak, J. H. Müller, J. Appel, and E. S. Polzik, “Toward quantum state tomography of a single polariton state of an atomic ensemble,” New J. Phys. 15, 015002 (2013).
[CrossRef]

S. L. Christensen, J. B. Béguin, E. Bookjans, H. L. Sørensen, J. H. Müller, J. Appel, and E. S. Polzik, “Quantum interference of a single spin excitation with a macroscopic atomic ensemble,” arxiv: [quant-ph] 1309.2514v2 (2013).

Béguin, J. B.

S. L. Christensen, J. B. Béguin, H. L. Sørensen, E. Bookjans, D. Oblak, J. H. Müller, J. Appel, and E. S. Polzik, “Toward quantum state tomography of a single polariton state of an atomic ensemble,” New J. Phys. 15, 015002 (2013).
[CrossRef]

S. L. Christensen, J. B. Béguin, E. Bookjans, H. L. Sørensen, J. H. Müller, J. Appel, and E. S. Polzik, “Quantum interference of a single spin excitation with a macroscopic atomic ensemble,” arxiv: [quant-ph] 1309.2514v2 (2013).

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

Bookjans, E.

S. L. Christensen, J. B. Béguin, H. L. Sørensen, E. Bookjans, D. Oblak, J. H. Müller, J. Appel, and E. S. Polzik, “Toward quantum state tomography of a single polariton state of an atomic ensemble,” New J. Phys. 15, 015002 (2013).
[CrossRef]

S. L. Christensen, J. B. Béguin, E. Bookjans, H. L. Sørensen, J. H. Müller, J. Appel, and E. S. Polzik, “Quantum interference of a single spin excitation with a macroscopic atomic ensemble,” arxiv: [quant-ph] 1309.2514v2 (2013).

Briegel, H. J.

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[CrossRef]

Buchler, B. C.

M. Hosseini, G. Campbell, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Unconditional room-temperature quantum memory,” Nature Phys. 7, 794–798 (2011).
[CrossRef]

Campbell, G.

M. Hosseini, G. Campbell, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Unconditional room-temperature quantum memory,” Nature Phys. 7, 794–798 (2011).
[CrossRef]

Cataliotti, F. S.

J. Petrovic, I. Herrera, P. Lombardi, F. Schaefer, and F. S. Cataliotti, “A multi-state interferometer on an atom chip,” New J. Phys. 15, 043002 (2013).
[CrossRef]

Choi, K.

C.-W. Chou, J. Laurat, H. Deng, K. Choi, H. De Riedmatten, D. Felinto, and H. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

Chou, C.-W.

C.-W. Chou, J. Laurat, H. Deng, K. Choi, H. De Riedmatten, D. Felinto, and H. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

Christensen, S. L.

S. L. Christensen, J. B. Béguin, H. L. Sørensen, E. Bookjans, D. Oblak, J. H. Müller, J. Appel, and E. S. Polzik, “Toward quantum state tomography of a single polariton state of an atomic ensemble,” New J. Phys. 15, 015002 (2013).
[CrossRef]

S. L. Christensen, J. B. Béguin, E. Bookjans, H. L. Sørensen, J. H. Müller, J. Appel, and E. S. Polzik, “Quantum interference of a single spin excitation with a macroscopic atomic ensemble,” arxiv: [quant-ph] 1309.2514v2 (2013).

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2010).
[CrossRef]

Cirac, J. I.

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[CrossRef]

Cook, R. J.

R. J. Cook and B. Shore, “Coherent dynamics of N-level atoms and molecules. III. An analytically soluble periodic case,” Phys. Rev. A 20, 539 (1979).
[CrossRef]

Cornell, E. A.

D. M. Harber, H. J. Lewandowski, J. M. McGuirk, and E. A. Cornell, “Effect of cold collisions on spin coherence and resonance shifts in a magnetically trapped ultracold gas,” Phys. Rev. A 66, 053616 (2002).
[CrossRef]

De Riedmatten, H.

C.-W. Chou, J. Laurat, H. Deng, K. Choi, H. De Riedmatten, D. Felinto, and H. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

Deng, H.

C.-W. Chou, J. Laurat, H. Deng, K. Choi, H. De Riedmatten, D. Felinto, and H. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

DiVincenzo, D. P.

D. P. DiVincenzo, “Quantum computation,” Science 270, 255–261 (1995).
[CrossRef]

Dür, W.

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[CrossRef]

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

Eisaman, M.

M. Eisaman, A. André, F. Massou, M. Fleischhauer, A. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438, 837–841 (2005).
[CrossRef] [PubMed]

Felinto, D.

C.-W. Chou, J. Laurat, H. Deng, K. Choi, H. De Riedmatten, D. Felinto, and H. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

Fernholz, T.

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nature Phys. 7, 13–16 (2011).
[CrossRef]

Fleischhauer, M.

M. Eisaman, A. André, F. Massou, M. Fleischhauer, A. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438, 837–841 (2005).
[CrossRef] [PubMed]

Fort, C.

F. Minardi, C. Fort, P. Maddaloni, M. Modugno, and M. Inguscio, “Time-domain atom interferometry across the threshold for Bose-Einstein condensation,” Phys. Rev. Lett. 87, 170401 (2001).
[CrossRef] [PubMed]

Hager, J.

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802 (2002).
[CrossRef]

Harber, D. M.

D. M. Harber, H. J. Lewandowski, J. M. McGuirk, and E. A. Cornell, “Effect of cold collisions on spin coherence and resonance shifts in a magnetically trapped ultracold gas,” Phys. Rev. A 66, 053616 (2002).
[CrossRef]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

Herrera, I.

J. Petrovic, I. Herrera, P. Lombardi, F. Schaefer, and F. S. Cataliotti, “A multi-state interferometer on an atom chip,” New J. Phys. 15, 043002 (2013).
[CrossRef]

Hosseini, M.

M. Hosseini, G. Campbell, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Unconditional room-temperature quantum memory,” Nature Phys. 7, 794–798 (2011).
[CrossRef]

Inguscio, M.

F. Minardi, C. Fort, P. Maddaloni, M. Modugno, and M. Inguscio, “Time-domain atom interferometry across the threshold for Bose-Einstein condensation,” Phys. Rev. Lett. 87, 170401 (2001).
[CrossRef] [PubMed]

Jensen, K.

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nature Phys. 7, 13–16 (2011).
[CrossRef]

Kimble, H.

H. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[CrossRef] [PubMed]

C.-W. Chou, J. Laurat, H. Deng, K. Choi, H. De Riedmatten, D. Felinto, and H. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

Krauter, H.

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nature Phys. 7, 13–16 (2011).
[CrossRef]

Lam, P. K.

M. Hosseini, G. Campbell, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Unconditional room-temperature quantum memory,” Nature Phys. 7, 794–798 (2011).
[CrossRef]

Laurat, J.

C.-W. Chou, J. Laurat, H. Deng, K. Choi, H. De Riedmatten, D. Felinto, and H. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

Lewandowski, H. J.

D. M. Harber, H. J. Lewandowski, J. M. McGuirk, and E. A. Cornell, “Effect of cold collisions on spin coherence and resonance shifts in a magnetically trapped ultracold gas,” Phys. Rev. A 66, 053616 (2002).
[CrossRef]

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

Lombardi, P.

J. Petrovic, I. Herrera, P. Lombardi, F. Schaefer, and F. S. Cataliotti, “A multi-state interferometer on an atom chip,” New J. Phys. 15, 043002 (2013).
[CrossRef]

Lukin, M. D.

M. Eisaman, A. André, F. Massou, M. Fleischhauer, A. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438, 837–841 (2005).
[CrossRef] [PubMed]

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802 (2002).
[CrossRef]

Maddaloni, P.

F. Minardi, C. Fort, P. Maddaloni, M. Modugno, and M. Inguscio, “Time-domain atom interferometry across the threshold for Bose-Einstein condensation,” Phys. Rev. Lett. 87, 170401 (2001).
[CrossRef] [PubMed]

Mair, A.

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802 (2002).
[CrossRef]

Massou, F.

M. Eisaman, A. André, F. Massou, M. Fleischhauer, A. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438, 837–841 (2005).
[CrossRef] [PubMed]

McGuirk, J. M.

D. M. Harber, H. J. Lewandowski, J. M. McGuirk, and E. A. Cornell, “Effect of cold collisions on spin coherence and resonance shifts in a magnetically trapped ultracold gas,” Phys. Rev. A 66, 053616 (2002).
[CrossRef]

Minardi, F.

F. Minardi, C. Fort, P. Maddaloni, M. Modugno, and M. Inguscio, “Time-domain atom interferometry across the threshold for Bose-Einstein condensation,” Phys. Rev. Lett. 87, 170401 (2001).
[CrossRef] [PubMed]

Modugno, M.

F. Minardi, C. Fort, P. Maddaloni, M. Modugno, and M. Inguscio, “Time-domain atom interferometry across the threshold for Bose-Einstein condensation,” Phys. Rev. Lett. 87, 170401 (2001).
[CrossRef] [PubMed]

Müller, J. H.

S. L. Christensen, J. B. Béguin, H. L. Sørensen, E. Bookjans, D. Oblak, J. H. Müller, J. Appel, and E. S. Polzik, “Toward quantum state tomography of a single polariton state of an atomic ensemble,” New J. Phys. 15, 015002 (2013).
[CrossRef]

S. L. Christensen, J. B. Béguin, E. Bookjans, H. L. Sørensen, J. H. Müller, J. Appel, and E. S. Polzik, “Quantum interference of a single spin excitation with a macroscopic atomic ensemble,” arxiv: [quant-ph] 1309.2514v2 (2013).

Nielsen, B. M.

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nature Phys. 7, 13–16 (2011).
[CrossRef]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2010).
[CrossRef]

Oblak, D.

S. L. Christensen, J. B. Béguin, H. L. Sørensen, E. Bookjans, D. Oblak, J. H. Müller, J. Appel, and E. S. Polzik, “Toward quantum state tomography of a single polariton state of an atomic ensemble,” New J. Phys. 15, 015002 (2013).
[CrossRef]

Owari, M.

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nature Phys. 7, 13–16 (2011).
[CrossRef]

Petrovic, J.

J. Petrovic, I. Herrera, P. Lombardi, F. Schaefer, and F. S. Cataliotti, “A multi-state interferometer on an atom chip,” New J. Phys. 15, 043002 (2013).
[CrossRef]

Phillips, D. F.

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802 (2002).
[CrossRef]

Plenio, M. B.

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nature Phys. 7, 13–16 (2011).
[CrossRef]

Polzik, E. S.

S. L. Christensen, J. B. Béguin, H. L. Sørensen, E. Bookjans, D. Oblak, J. H. Müller, J. Appel, and E. S. Polzik, “Toward quantum state tomography of a single polariton state of an atomic ensemble,” New J. Phys. 15, 015002 (2013).
[CrossRef]

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nature Phys. 7, 13–16 (2011).
[CrossRef]

S. L. Christensen, J. B. Béguin, E. Bookjans, H. L. Sørensen, J. H. Müller, J. Appel, and E. S. Polzik, “Quantum interference of a single spin excitation with a macroscopic atomic ensemble,” arxiv: [quant-ph] 1309.2514v2 (2013).

Schaefer, F.

J. Petrovic, I. Herrera, P. Lombardi, F. Schaefer, and F. S. Cataliotti, “A multi-state interferometer on an atom chip,” New J. Phys. 15, 043002 (2013).
[CrossRef]

Serafini, A.

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nature Phys. 7, 13–16 (2011).
[CrossRef]

Shore, B.

R. J. Cook and B. Shore, “Coherent dynamics of N-level atoms and molecules. III. An analytically soluble periodic case,” Phys. Rev. A 20, 539 (1979).
[CrossRef]

Sørensen, H. L.

S. L. Christensen, J. B. Béguin, H. L. Sørensen, E. Bookjans, D. Oblak, J. H. Müller, J. Appel, and E. S. Polzik, “Toward quantum state tomography of a single polariton state of an atomic ensemble,” New J. Phys. 15, 015002 (2013).
[CrossRef]

S. L. Christensen, J. B. Béguin, E. Bookjans, H. L. Sørensen, J. H. Müller, J. Appel, and E. S. Polzik, “Quantum interference of a single spin excitation with a macroscopic atomic ensemble,” arxiv: [quant-ph] 1309.2514v2 (2013).

Sparkes, B. M.

M. Hosseini, G. Campbell, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Unconditional room-temperature quantum memory,” Nature Phys. 7, 794–798 (2011).
[CrossRef]

Walsworth, R. L.

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802 (2002).
[CrossRef]

Wasilewski, W.

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nature Phys. 7, 13–16 (2011).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

a) Experimental sequence. The condensate consists of atoms in |F = 2, mF = +2〉 state. Upon release from the magnetic trap the atomic cloud is left free to fall in the homogeneous bias magnetic field B. After 100 μs the Raman coupling is applied for a time τ′ = 6.2 μs. The resultant superposition of spin levels is left free to evolve for a time T ∼ 1 – 100 μs during which atoms in different mF states acquire differential phases ϕi. Then the RF coupling is applied (pulse duration τ = 8.3 μs), followed by the application of a magnetic field gradient to spatially separate the different mF states. Finally, the population distribution is detected by absorption imaging. b) Energy levels of the D2 line of 87Rb (vertical energy axis not to scale) and field couplings used in the experiment.

Fig. 2
Fig. 2

Scheme of the experimental set-up. The generation of the Raman beams is obtained by merging two beams (red) on a polarizing beam-splitter (PBS1). The magnetization axis of the sample is set parallel to one of the two linear polarizations outgoing the PBS1, which is hence seen by the atoms as π-polarized, while the orthogonal one is seen as a sum of the opposite σ polarizations. Due to the Zeeman splitting induced by the bias magnetic field B, the component of the beam with the ”wrong” σ polarization is out of resonance for the two-photon transition. After passing through the vacuum cell (blue), the two polarization components are mixed by means of a half-waveplate (λ/2) and a second polarizing beam-splitter (PBS2). This operation enables the detection of a beat note on the photodiode detector (PD) which reproduces the frequency difference and the relative phase between the two components. Both the magnetic trap and the Stern-Gerlach gradient are obtained by the same current-carrying z-shaped wire on the chip [13]. The absorption imaging beam is shown in green.

Fig. 3
Fig. 3

Experimental results: a), b) - population distribution as read at the output of the interferometer versus beat note phase read by the photodiode (histograms). In a) the internal state populations are separately shown for the five Zeeman states at delay T = 1.3 μs. For the stretched states (mF = ±2), the maximum slope we achieve is (0.64 ± 0.07) [rad]−1. In b) population distribution for different interrogation time T = 1.3; 1.4; 1.7 μs (from top to bottom respectively) are reported. By changing the delay time T between the two pulses it is possible to shift the phase region for which the maximum sensitivity is obtained. The periodicity of the fringe shift is given by the fundamental frequency of the system, that is the Zeeman splitting ΔE/ħ = 2.171 MHz. In all the graphs, solid lines represent population distributions obtained by numerical calculation of the evolution of the initial state in the density matrix representation.We have reported the results obtained for the decay rate γ = 1 kHz. c) - fringe contrast in the mF = ±2 states as function of the time delay T. Fitting the data with an exponential decay (solid line) we obtain a decay time constant of t̃ = (61 ± 9) μs, which is in qualitative agreement with the trend predicted by the numerical simulations. The shaded area encloses the trend for decay rates γ between 1 kHz and 1.5 kHz (γ = 1 kHz → t̃ ∼ 75 μs, γ = 1.5 kHz → t̃ ∼ 50 μs).

Equations (3)

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J = R ( Ω τ ) P ( T ) R ( Ω τ ) , J j , k = l = 1 5 R j , l ( Ω τ ) e i ( l 1 ) Δ E T R l , k ( Ω τ ) ,
J j , k = l = 1 5 R j , l ( A ) e i ( l 1 ) Δ E ( T + Δ E δ ϕ ) R l , k ( A ) .
T ( δ ϕ ) = Δ E δ ϕ .

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