## Delay of squeezing and entanglement using electromagnetically induced transparency in a vapour cell

Optics Express, Vol. 16, Issue 10, pp. 7369-7381 (2008)

http://dx.doi.org/10.1364/OE.16.007369

Acrobat PDF (731 KB)

### Abstract

We demonstrate experimentally the delay of squeezed light and entanglement using Electromagnetically Induced Transparency (EIT) in a rubidium vapour cell. We perform quadrature amplitude measurements of the probe field and find no appreciable excess noise from the EIT process. From input squeezing of 3.2±0.5 dB at low sideband frequencies, we observed the survival of 2.0±0.5 dB of squeezing at the EIT output. By splitting the squeezed light on a beam-splitter, we generated biased entanglement between two beams. We transmit one of the entangled beams through the EIT cell and correlate the quantum statistics of this beam with its entangled counterpart. We experimentally observed a 2.2±0.5*µ*s delay of the biased entanglement and obtained a preserved degree of wavefunction inseparability of 0.71±0.01, below the unity value for separable states.

© 2008 Optical Society of America

## 1. Introduction.

1. C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin,“Quantum Repeaters with Photon Pair Sources and Multimode Memories,” Phys. Rev. Lett. **98**, 190503 (2007). [CrossRef] [PubMed]

2. L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature **414**, 413 (2001). [CrossRef] [PubMed]

3. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature **409**, 46 (2001). [CrossRef] [PubMed]

4. M. Fleischhauer and M. D. Lukin, “Dark-State Polaritons in Electromagnetically Induced Transparency,” Phys. Rev. Lett. **84**, 5094 (2000). [CrossRef] [PubMed]

5. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature **397**, 594 (1999). [CrossRef]

6. 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 (2001). [CrossRef] [PubMed]

7. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. **86**, 783 (2001). [CrossRef] [PubMed]

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

9. T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature **438**, 833 (2005). [CrossRef] [PubMed]

10. D. Akamatsu, Y. Yokoi, M. Arikawa, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Ultraslow propagation of squeezed vacuum pulses with electromagnetically induced transparency,” Phys. Rev. Lett. **99**, 153602 (2007). [CrossRef] [PubMed]

11. J. Appel, E. Figueroa, D. Korystov, M. Lobino, and A. I. Lvovsky, “Quantum memory for squeezed light,” Phys. Rev. Lett. **100**, 093602 (2008). [CrossRef] [PubMed]

12. K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and Retrieval of a Squeezed Vacuum,” Phys. Rev. Lett. **100**, 093601 (2008). [CrossRef] [PubMed]

13. M. Arikawa, K. Honda, D. Akamatsu, Y. Yokoi, K. Akiba, S. Nagatsuka, A. Furusawa, and M. Kozuma, “Observation of electromagnetically induced transparency for a squeezed vacuum with the time domain method,” Opt. Express **15**, 11849 (2007). [CrossRef] [PubMed]

13. M. Arikawa, K. Honda, D. Akamatsu, Y. Yokoi, K. Akiba, S. Nagatsuka, A. Furusawa, and M. Kozuma, “Observation of electromagnetically induced transparency for a squeezed vacuum with the time domain method,” Opt. Express **15**, 11849 (2007). [CrossRef] [PubMed]

10. D. Akamatsu, Y. Yokoi, M. Arikawa, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Ultraslow propagation of squeezed vacuum pulses with electromagnetically induced transparency,” Phys. Rev. Lett. **99**, 153602 (2007). [CrossRef] [PubMed]

*µ*s. Appel,

*et al.*[11

11. J. Appel, E. Figueroa, D. Korystov, M. Lobino, and A. I. Lvovsky, “Quantum memory for squeezed light,” Phys. Rev. Lett. **100**, 093602 (2008). [CrossRef] [PubMed]

*et al.*[12

12. K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and Retrieval of a Squeezed Vacuum,” Phys. Rev. Lett. **100**, 093601 (2008). [CrossRef] [PubMed]

*µs*in gas cell, 0.21 dB of squeezing was retrieved from an input of 1.86 dB [11

11. J. Appel, E. Figueroa, D. Korystov, M. Lobino, and A. I. Lvovsky, “Quantum memory for squeezed light,” Phys. Rev. Lett. **100**, 093602 (2008). [CrossRef] [PubMed]

*µ*s [12

12. K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and Retrieval of a Squeezed Vacuum,” Phys. Rev. Lett. **100**, 093601 (2008). [CrossRef] [PubMed]

^{87}Rb cell filled with buffer gas. In our second experiment, we demonstrate the delay and preservation of continuous variable entanglement by transmission through the EIT medium. Our scheme for delaying entanglement is shown in Fig 1. By splitting a single squeezed light beam, biased entanglement is generated between the two output beams of the beam-splitter [15]. We send one of the beams through the EIT vapour cell and perform joint measurements of the quadrature amplitudes of both beams. By analysing the quantum statistics of the joint measurements, we can directly calculate the amount of delay and entanglement between the two beams. Delay of entanglement between remote atomic ensembles was achieved in the continuous variable regime using the off-resonant Faraday rotation [16

16. B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature **432**, 482 (2004). [CrossRef] [PubMed]

## 2. EIT preparation.

*D*

_{1}line of

^{87}Rb (795 nm), which has the level structure shown in Fig. 1(ii). The atomic levels used were the |5

^{2}

*S*

_{1/2},

*F*=2〉 for the ground state and the |5

_{g}^{2}

*P*

_{1/2},

*F*=2〉 for the excited state. In steady state, the coupling beam accessed the |5

_{e}^{2}

*S*

_{1/2},

*F*=2,

_{g}*m*=0〉 Zeeman ground state sublevels, and the probe beam the |5

_{F}^{2}

*S*

_{1/2},

*F*=2,

_{g}*m*=-2〉 sublevel. Both beams were derived from a Ti:Sapphire laser (Coherent MBR). The degeneracy of the Zeeman sublevels was broken using an externally applied longitudinal magnetic field of 8.5 Gauss. To maintain the two photon resonance condition required for EIT, the control beam was frequency shifted by 6 MHz with respect to the probe light using two cascaded AOMs in a double-pass configuration. This non-degenerate configuration greatly simplifies the alignment procedure used to optimize the EIT. When the beams are frequency degenerate, residual polarization cross-coupling between the probe and the control beams leads to parasitic low frequency fluctuations of the beam powers. The introduced Zeeman shift between the ground states shifts these fluctuations to a frequency of 6 MHz, which is well outside the measurement bandwidth.

_{F}^{87}Rb, heated to 70°C and filled with 5 Torr of Helium buffer gas. The cell is AR coated on the outside windows, which gives 92% transmission in the absence of any active atoms. This represents the best possible transmission our EIT system can achieve. In order to reduce stray magnetic fields,

*µ*-metal shielding was used around the cell. The diameters of the control (

*C*) and probe (

*P*) beams were around 2 cm and 0.3 cm inside the vapour cell, respectively. A 20 mW/cm

^{2}repump beam (

*R*) from an external cavity diode laser was used to bring atoms from the F=1 ground state hyperfine level to the F=2 ground state (as depicted in Fig. 1(ii)). The repumping enhances the optical depth seen by the weak probe field without significant impact on the ground state coherence.

## 3. Noise measurement and interpretation.

17. M. T. L. Hsu, G. Hétet, O. Glöckl, J. J. Longdell, B. C. Buchler, H.-A. Bachor, and P. K. Lam, “Quantum Study of Information Delay in Electromagnetically Induced Transparency,” Phys. Rev. Lett. **97**, 183601 (2006). [CrossRef] [PubMed]

*m*=-2 Zeeman sublevel and/or inelastic collisions with the cell walls. Both these mechanisms result in non-negligible atomic populations of Zeeman sublevels that are not interacting with the probe.

_{F}*m*=-1 and

_{F}*m*=0. It has been shown that this situation will give rise to gain in the probe mode [18

_{F}18. G. Hétet, A. Peng, M. T. Johnsson, J. J. Hope, and P. K. Lam, “Characterization of electromagnetically-induced-transparency-based continuous-variable quantum memories,” Phys. Rev. A , **77**, 012323 (2008). [CrossRef]

17. M. T. L. Hsu, G. Hétet, O. Glöckl, J. J. Longdell, B. C. Buchler, H.-A. Bachor, and P. K. Lam, “Quantum Study of Information Delay in Electromagnetically Induced Transparency,” Phys. Rev. Lett. **97**, 183601 (2006). [CrossRef] [PubMed]

19. E. Figueroa, F. Vewinger, J. Appel, and A. I. Lvovsky, “Decoherence of electromagnetically induced transparency in atomic vapor” Opt. Lett. **31**, 2625 (2006). [CrossRef] [PubMed]

## 4. Squeezing preparation.

*D*

_{1}line was achieved recently in several laboratories using optical parametric oscillators (OPO) [11

**100**, 093602 (2008). [CrossRef] [PubMed]

14. G. Hétet, O. Glöckl, K. A. Pilypas, C. C. Harb, B. C. Buchler, H.-A. Bachor, and P. K. Lam, “Squeezed light for bandwidth limited atom optics experiments at the Rubidium D1 line,” J. Phys. B, At. Mol. Opt. Phys. **40**221 (2007). [CrossRef]

21. T. Tanimura, D. Akamatsu, Y. Yokoi, A. Furusawa, and M. Kozuma, “Generation of a squeezed vacuum resonant on a rubidium D1 line with periodically poled KTiOPO4,” Opt. Lett. **31**, 2344, (2006). [CrossRef] [PubMed]

14. G. Hétet, O. Glöckl, K. A. Pilypas, C. C. Harb, B. C. Buchler, H.-A. Bachor, and P. K. Lam, “Squeezed light for bandwidth limited atom optics experiments at the Rubidium D1 line,” J. Phys. B, At. Mol. Opt. Phys. **40**221 (2007). [CrossRef]

22. K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E McClelland, “Quantum noise locking,” J. Opt. B: Quantum Semiclass. Opt. **7**, S421(2005). [CrossRef]

23. C. Schori, J. Sørensen, and E. S. Polzik, “Narrow-band frequency tunable light source of continuous quadrature entanglement,” Phys. Rev. A **66**, 033802 (2002). [CrossRef]

24. J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, “Compact source of Einstein-Podolsky-Rosen entanglement and squeezing at very low noise frequencies,” Phys. Rev. A **70**, 042315 (2004). [CrossRef]

25. K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, “Squeezing in the Audio Gravitational-Wave Detection Band,” Phys. Rev. Lett. **93**, 161105 (2004). [CrossRef] [PubMed]

_{00}beam that travelled in the reverse direction around the OPO cavity. It transpired that this beam was partially reflected by the surfaces of the OPO crystal leading to some residual coherent amplitude in the squeezed output. To avoid this problem a frequency shifted backwards propagating TEM

_{02}mode was used to lock the OPO cavity, as shown in Fig. 1(i). The combination of noise-locking and a frequency shifted OPO locking beam allowed us to produce stably locked squeezing down to 200 Hz.

## 5. Squeezed light propagation through an EIT window.

26. A. Peng, M. Johnsson, W. P. Bowen, P. K. Lam, H.-A. Bachor, and J. J. Hope, “Squeezing and entanglement delay using slow light,” Phys. Rev. A **71**, 033809 (2004). [CrossRef]

## 6. Criteria for continuous variable entanglement.

*a*and

*b*, can be mixed on a beam-splitter with a

*π*/2 phase difference between them [27

27. Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. **68**, 3663 (1992). [CrossRef] [PubMed]

28. W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, “Experimental Investigation of Criteria for Continuous Variable Entanglement,” Phys. Rev. Lett. **90**, 043601 (2003). [CrossRef] [PubMed]

29. W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, “Experimental characterization of continuous-variable entanglement,” Phys. Rev. A **69**, 012304 (2004). [CrossRef]

*c*and

*d*, can be performed using two homodyne detectors measuring the uncertainty of the quadrature operators X̂

^{±}

*and X̂*

_{d}^{±}

*. It can be shown that in the case of*

_{c}*a*and

*b*being pure squeezed states, measuring any quadrature of

*c*will allow us to infer the corresponding quadrature of

*d*with uncertainty better than the quantum noise limit (QNL).

^{±}

*given knowledge of the signal X̂*

_{c}^{±}

*can be written as [30*

_{d}30. M. D. Reid and P. D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett. **60**, 2731–2733 (1988). [CrossRef] [PubMed]

*V*

^{±}

*is the variance of the amplitude/phase quadrature fluctuations of the beams*

_{c,d}*c*and

*d*. When using amplitude squeezed beams as input states, the conditional variance between

*c*and

*d*will be below the QNL, given by V

^{±}(

*c*|

*d*)=1, indicating a non-classical correlation between them.

*c*and

*d*. The perimeter of the ellipses shows

*σ*

^{±}

*given by*

_{θ}^{±}

*is the variance of the data projected onto axes at an angle*

_{θ}*θ*and C

^{±}

*=|〈X̂*

_{θ}^{±}

*X̂*

_{θ}^{±}

_{θ+π/2}〉|

^{2}/V

^{±}

*V*

_{θ}^{±}

_{θ+π/2}is the correlation also measured along the rotated axes. For the situation shown in Fig. 3(i), we find that

*σ*

^{±}

*is an ellipse with its axis oriented at +*

_{θ}*π*/4 for the amplitude quadratures and -

*π*/4 for phase quadratures. In Fig. 3(i) these are shown in red.

^{±}(

*c*|

*d*) can be found from σ

^{±}

*by measuring the square of the radius of the ellipse at the point where it crosses the horizontal axis, that is V*

_{θ}^{±}(

*c*|

*d*)=(σ

^{±}

_{θ=0})

^{2}. V

^{±}(

*d*|

*c*) however will be found from the radius of ellipse at the points where it crosses the vertical axis, V

^{±}(

*d*|

*c*)=(σ

^{±}

_{θ=π/2})

^{2}. The QNL is obtained by replacing the squeezed beams by vacuum states. The QNL forms circles of unity radius as shown by the perimeters of the blue circles in Fig. 3(i). For the case in this figure, it is clear that V

^{±}(

*d*|

*c*)=V

^{±}(

*c*|

*d*)<1.

*θ*=-

*π*/4 and

*θ*=

*π*/4, for the amplitude and phase quadratures respectively, the correlations lie inside the unity circle and reaches a minimum. To see what these minima mean, one can calculate σ

^{±}

*as a function of the rotation angle (*

_{θ}*θ*) and the input variances. We find

*c*and

*d*and the variances of the original inputs

*a*and

*b*. These quantities are useful for the calculation of the entanglement figures of merit.

30. M. D. Reid and P. D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett. **60**, 2731–2733 (1988). [CrossRef] [PubMed]

31. L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. **84**, 2722 (2000). [CrossRef] [PubMed]

32. R. Simon, “Peres-Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. **84**, 2726 (2000). [CrossRef] [PubMed]

^{+}(

*c*|

*d*)V

^{-}(

*c*|

*d*)<1, for entangled beams. We can write the product of the conditional variances in terms of the input beams at the beam-splitter and find that

^{+}

_{(a,b)}V

^{-}

_{(a,b)}=1, V

^{+}

*<1 and V*

_{a}^{+}

*<1. Strong entanglement will be obtained in the regimes of large and pure squeezing. Entanglement can also be obtained when only one input beam is a pure squeezed state and the other input beam is vacuum (e.g. V*

_{b}^{+}

*<1<V*

_{a}^{-}

*and V*

_{a}^{±}

*=1). This situation is depicted Fig. 3(ii). The state generated in this way is called a biased entangled state [15] because of the asymmetry at the two output quadratures. The correlation plots indeed show that in this case one has V*

_{b}^{+}(

*c*|

*d*)=1 and V

^{-}(

*c*|

*d*)<1, so the EPR inequality still holds.

*c*to

*d*or

*d*to

*c*. When the losses are different on each arm, like in the situation depicted in Fig. 3(iii), the conditional variance of

*d*given

*c*is larger than for

*c*given

*d*. These different ways to infer are referred to as direct reconciliation and reverse reconciliation respectively [33]. This gives rise to two numbers for EPR correlations. This is seen graphically in the corresponding correlation plots (Fig. 3(iii)) where the ellipses have both been rotated clockwise by an amount depending on the loss on the beam

*c*. The difference between the V

^{±}(

*c*|

*d*) and V

^{±}(

*d*|

*c*) appears clearly.

31. L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. **84**, 2722 (2000). [CrossRef] [PubMed]

31. L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. **84**, 2722 (2000). [CrossRef] [PubMed]

*i*,

*j*} ∈ {+,-}. Before the inseparability criterion can be applied, the correlation matrix has to be in standard form II, which can be achieved by application of the appropriate local-linear-unitary-Bogoliubov-operations (local rotation and squeezing operations) [31

**84**, 2722 (2000). [CrossRef] [PubMed]

28. W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, “Experimental Investigation of Criteria for Continuous Variable Entanglement,” Phys. Rev. Lett. **90**, 043601 (2003). [CrossRef] [PubMed]

29. W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, “Experimental characterization of continuous-variable entanglement,” Phys. Rev. A **69**, 012304 (2004). [CrossRef]

*±X*

_{c}*)= min〈(X*

_{d}*±X*

_{c}*)*

_{d}^{2}〉. This last quantity can be evaluated quite easily, for example, from the conditional deviation ellipse Fig. 3(i). From the graph, we see that V(X

^{+}

*±X*

_{c}^{+}

*)=(σ*

_{d}^{+}

_{-π/4})

^{2}=V

^{+}

*which is the squeezed quadrature of beam*

_{a}*a*. On the other hand, V(X

^{-}

*± X*

_{c}^{-}

*)=(σ*

_{d}^{-}

_{π/4})

^{2}=V

^{+}

*, which is the squeezed quadrature of beam*

_{b}*b*. In this situation 𝓘<1 so the state is not separable. When the losses are different on both arms, local unitary transformations have to be done to the correlation matrix to express it in standard form II. This process has a very simple graphical interpretation. In the case of unequal losses shown in Fig. 3(iii), the minima of the ellipses no longer appear on the diagonals at

*θ*=±

*π*/4. The local transformations are just used to reorient the ellipses so that the minima will again appear on the diagonals. The local transformations do not change the value of these minima, so we can always find 𝓘 directly from the minima of the conditional deviation ellipses without local transformations.

## 7. Entanglement measurement.

^{+}(

*c*|

*d*)V

^{-}(

*c*|

*d*)=0.80×1.60=1.28±0.01 and V

^{+}(

*d*|

*c*)V

^{-}(

*d*|

*c*)=0.80×1.62=1.30±0.01. The inference from

*d*to

*c*gives a slightly larger EPR value due to small extra losses from the cell windows and the difference in the homodyne visibility. These values are above 1, so according to the EPR criterion there is no entanglement. This is primarily due to the impurity of our squeezed state. Internal loss inside the OPO cavity always leads to squeezed states with non-minimum uncertainty and, as discussed, the EPR criterion is sensitive to the purity of the initial squeezing.

^{+}(

*c*|

*d*)V

^{-}(

*c*|

*d*)=1.01×1.25=1.26±0.01 and V

^{+}(

*d*|

*c*)V

^{-}(

*d*|

*c*)=0.80×4.05=3.24±0.01. We note that the presence of loss in the EIT medium does not change the conditional variance significantly when inferring from the beam propagating in free space.

_{±}σ

*. This value is higher than the off-resonance case but still below 1, demonstrating that our EIT system preserves inseparability.*

_{θ}*g*(

*τ*)=〈X

^{+}

*(*

_{c}*t*)X

^{+}

*(*

_{d}*t*-

*τ*)〉 as a function of the delay,

*τ*, between

*c*and

*d*. By looking for a peak correlation as a function of

*τ*we can find the delay introduced by the EIT transmission. Figure 5(a) represents the degree of correlation between

*c*and

*d*with the atoms off (i) and on resonance (ii). This shows that EIT delayed the transmission of beam

*c*by 2.2

*µ*s. Some amount of correlation is clearly lost in transmission through the EIT as the peak of curve (ii) is substantially lower than case with no EIT. Figure 5(b) compares the amplitude quadrature conditional deviations with and without EIT. The reduced correlation is also clear in this figure.

*et al.*[34

34. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Coherent control of vacuum squeezing in the gravitational-wave detection band,” Phys. Rev. Lett. **97**, 011101 (2006). [CrossRef] [PubMed]

## 8. Conclusion.

^{87}Rb vapour in the presence of buffer gas. Using a buffer gas allowed us to obtain quantum noise limited delay, removing the excess noise observed previously [17

17. M. T. L. Hsu, G. Hétet, O. Glöckl, J. J. Longdell, B. C. Buchler, H.-A. Bachor, and P. K. Lam, “Quantum Study of Information Delay in Electromagnetically Induced Transparency,” Phys. Rev. Lett. **97**, 183601 (2006). [CrossRef] [PubMed]

*µ*s. The wavefunction inseparability after EIT delay of one half of the entangled state was measured to be 0.71±0.01. This result is a promising step towards the reversible storage of continuous variable quantum information, a necessary milestone for many quantum information protocols.

## Acknowledgments

## References and links

1. | C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin,“Quantum Repeaters with Photon Pair Sources and Multimode Memories,” Phys. Rev. Lett. |

2. | L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature |

3. | E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature |

4. | M. Fleischhauer and M. D. Lukin, “Dark-State Polaritons in Electromagnetically Induced Transparency,” Phys. Rev. Lett. |

5. | L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature |

6. | 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 |

7. | D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. |

8. | M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature |

9. | T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature |

10. | D. Akamatsu, Y. Yokoi, M. Arikawa, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Ultraslow propagation of squeezed vacuum pulses with electromagnetically induced transparency,” Phys. Rev. Lett. |

11. | J. Appel, E. Figueroa, D. Korystov, M. Lobino, and A. I. Lvovsky, “Quantum memory for squeezed light,” Phys. Rev. Lett. |

12. | K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and Retrieval of a Squeezed Vacuum,” Phys. Rev. Lett. |

13. | M. Arikawa, K. Honda, D. Akamatsu, Y. Yokoi, K. Akiba, S. Nagatsuka, A. Furusawa, and M. Kozuma, “Observation of electromagnetically induced transparency for a squeezed vacuum with the time domain method,” Opt. Express |

14. | G. Hétet, O. Glöckl, K. A. Pilypas, C. C. Harb, B. C. Buchler, H.-A. Bachor, and P. K. Lam, “Squeezed light for bandwidth limited atom optics experiments at the Rubidium D1 line,” J. Phys. B, At. Mol. Opt. Phys. |

15. | W. P. Bowen, P. K. Lam, and T. C. Ralph, “Biased EPR entanglement and its application to teleportation,” J. Mod. Opt. |

16. | B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature |

17. | M. T. L. Hsu, G. Hétet, O. Glöckl, J. J. Longdell, B. C. Buchler, H.-A. Bachor, and P. K. Lam, “Quantum Study of Information Delay in Electromagnetically Induced Transparency,” Phys. Rev. Lett. |

18. | G. Hétet, A. Peng, M. T. Johnsson, J. J. Hope, and P. K. Lam, “Characterization of electromagnetically-induced-transparency-based continuous-variable quantum memories,” Phys. Rev. A , |

19. | E. Figueroa, F. Vewinger, J. Appel, and A. I. Lvovsky, “Decoherence of electromagnetically induced transparency in atomic vapor” Opt. Lett. |

20. | J. Cviklinski, J. Ortalo, A. Bramati, M. Pinard, and E. Giacobino, “Reversible Quantum Interface for Tunable Single-sideband Modulation” arXiv 0711.0264 (2007). |

21. | T. Tanimura, D. Akamatsu, Y. Yokoi, A. Furusawa, and M. Kozuma, “Generation of a squeezed vacuum resonant on a rubidium D1 line with periodically poled KTiOPO4,” Opt. Lett. |

22. | K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E McClelland, “Quantum noise locking,” J. Opt. B: Quantum Semiclass. Opt. |

23. | C. Schori, J. Sørensen, and E. S. Polzik, “Narrow-band frequency tunable light source of continuous quadrature entanglement,” Phys. Rev. A |

24. | J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, “Compact source of Einstein-Podolsky-Rosen entanglement and squeezing at very low noise frequencies,” Phys. Rev. A |

25. | K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, “Squeezing in the Audio Gravitational-Wave Detection Band,” Phys. Rev. Lett. |

26. | A. Peng, M. Johnsson, W. P. Bowen, P. K. Lam, H.-A. Bachor, and J. J. Hope, “Squeezing and entanglement delay using slow light,” Phys. Rev. A |

27. | Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. |

28. | W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, “Experimental Investigation of Criteria for Continuous Variable Entanglement,” Phys. Rev. Lett. |

29. | W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, “Experimental characterization of continuous-variable entanglement,” Phys. Rev. A |

30. | M. D. Reid and P. D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett. |

31. | L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. |

32. | R. Simon, “Peres-Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. |

33. | F. Grosshans and P. Grangier, “Reverse reconciliation protocols for quantum cryptography with continuous variables” quant-ph/0204127, (2002). |

34. | H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Coherent control of vacuum squeezing in the gravitational-wave detection band,” Phys. Rev. Lett. |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.6570) Quantum optics : Squeezed states

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: March 25, 2008

Revised Manuscript: May 5, 2008

Manuscript Accepted: May 5, 2008

Published: May 6, 2008

**Citation**

G. Hètet, B. C. Buchler, O. Glöeckl, M. T. L. Hsu, A. M. Akulshin, H. A. Bachor, and P. K. Lam, "Delay of squeezing and entanglement
using electromagnetically induced
transparency in a vapour cell," Opt. Express **16**, 7369-7381 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-10-7369

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### References

- C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin,"Quantum repeaters with photon pair sources and multimode memories," Phys. Rev. Lett. 98, 190503 (2007). [CrossRef] [PubMed]
- L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, "Long-distance quantum communication with atomic ensembles and linear optics," Nature 414, 413 (2001). [CrossRef] [PubMed]
- E. Knill, R. Laflamme, and G. J. Milburn,"A scheme for efficient quantum computation with linear optics," Nature 409, 46 (2001). [CrossRef] [PubMed]
- M. Fleischhauer and M. D. Lukin, "Dark-State Polaritons in electromagnetically induced transparency," Phys. Rev. Lett. 84, 5094 (2000). [CrossRef] [PubMed]
- L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas," Nature 397, 594 (1999). [CrossRef]
- 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 (2001). [CrossRef] [PubMed]
- D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, "Storage of light in atomic vapor," Phys. Rev. Lett. 86, 783 (2001). [CrossRef] [PubMed]
- M. D. Eisaman, A. Andr�??e, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, "Electromagnetically induced transparency with tunable single-photon pulses," Nature 438, 837 (2005). [CrossRef] [PubMed]
- T. Chaneliere, D. N. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, "Storage and retrieval of single photons transmitted between remote quantum memories," Nature 438, 833 (2005). [CrossRef] [PubMed]
- D. Akamatsu, Y. Yokoi, M. Arikawa, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, "Ultraslow propagation of squeezed vacuum pulses with electromagnetically induced transparency," Phys. Rev. Lett. 99, 153602 (2007). [CrossRef] [PubMed]
- J. Appel, E. Figueroa, D. Korystov, M. Lobino and A. I. Lvovsky, "Quantum memory for squeezed light," Phys. Rev. Lett. 100, 093602 (2008). [CrossRef] [PubMed]
- K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa and M. Kozuma, "Storage and Retrieval of a Squeezed Vacuum," Phys. Rev. Lett. 100, 093601 (2008). [CrossRef] [PubMed]
- M. Arikawa, K. Honda, D. Akamatsu, Y. Yokoi, K. Akiba, S. Nagatsuka, A. Furusawa, and M. Kozuma, "Observation of electromagnetically induced transparency for a squeezed vacuum with the time domain method," Opt. Express 15, 11849 (2007). [CrossRef] [PubMed]
- G. Hetet, O. Glockl, K. A . Pilypas, C. C. Harb, B. C . Buchler, H.-A. Bachor, and P. K . Lam, "Squeezed light for bandwidth limited atom optics experiments at the Rubidium D1 line," J. Phys. B At. Mol. Opt. Phys. 40, 221 (2007). [CrossRef]
- W. P. Bowen, P. K. Lam, and T. C. Ralph, "Biased EPR entanglement and its application to teleportation," J. Mod. Opt. 50, 801 (2003).
- B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, "Experimental demonstration of quantum memory for light," Nature 432, 482 (2004). [CrossRef] [PubMed]
- M. T. L. Hsu, G. Hetet, O. Glockl, J. J. Longdell, B. C. Buchler,H.-A. Bachor,P. K. Lam, "Quantum study of information delay in electromagnetically induced transparency," Phys. Rev. Lett. 97, 183601 (2006). [CrossRef] [PubMed]
- G. Hetet, A . Peng, M. T. Johnsson, J. J . Hope, and P. K . Lam, "Characterization of electromagnetically-inducedtransparency-based continuous-variable quantum memories," Phys. Rev. A, 77, 012323 (2008). [CrossRef]
- E. Figueroa, F. Vewinger, J. Appel, and A. I. Lvovsky, "Decoherence of electromagnetically induced transparency in atomic vapor," Opt. Lett. 31, 2625 (2006). [CrossRef] [PubMed]
- J. Cviklinski, J. Ortalo, A. Bramati, M. Pinard, and E. Giacobino, "Reversible Quantum Interface for Tunable Single-sideband Modulation," arXiv 0711.0264 (2007).
- T. Tanimura, D. Akamatsu, Y. Yokoi, A. Furusawa and M. Kozuma, "Generation of a squeezed vacuum resonant on a rubidium D1 line with periodically poled KTiOPO4," Opt. Lett. 31, 2344, (2006) [CrossRef] [PubMed]
- K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E McClelland, "Quantum noise locking," J. Opt. B: Quantum Semiclass. Opt. 7, S421(2005). [CrossRef]
- C. Schori, J. Sørensen, and E. S. Polzik, "Narrow-band frequency tunable light source of continuous quadrature entanglement," Phys. Rev. A 66, 033802 (2002). [CrossRef]
- J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, "Compact source of Einstein-Podolsky-Rosen entanglement and squeezing at very low noise frequencies," Phys. Rev. A 70, 042315 (2004). [CrossRef]
- K. McKenzie, N. Grosse,W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland and P. K. Lam, "Squeezing in the Audio Gravitational-Wave Detection Band," Phys. Rev. Lett. 93, 161105 (2004). [CrossRef] [PubMed]
- A. Peng, M. Johnsson, W. P. Bowen, P. K. Lam, H.-A. Bachor, and J. J. Hope, "Squeezing and entanglement delay using slow light," Phys. Rev. A 71, 033809 (2004). [CrossRef]
- Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663 (1992). [CrossRef] [PubMed]
- W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental Investigation of Criteria for Continuous Variable Entanglement," Phys. Rev. Lett. 90, 043601 (2003). [CrossRef] [PubMed]
- W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental characterization of continuous-variable entanglement," Phys. Rev. A 69, 012304 (2004). [CrossRef]
- M. D. Reid and P. D. Drummond, "Quantum correlations of phase in nondegenerate parametric oscillation," Phys. Rev. Lett. 60, 2731-2733 (1988). [CrossRef] [PubMed]
- L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, "Inseparability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2722 (2000). [CrossRef] [PubMed]
- R. Simon, "Peres-Horodecki separability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2726 (2000). [CrossRef] [PubMed]
- F. Grosshans and P. Grangier, "Reverse reconciliation protocols for quantum cryptography with continuous variables" quant-ph/0204127, (2002).
- H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "�??Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006). [CrossRef] [PubMed]

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