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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 19 — Sep. 17, 2007
  • pp: 11849–11854
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Observation of electromagnetically induced transparency for a squeezed vacuum with the time domain method

M. Arikawa, K. Honda, D. Akamatsu, Y. Yokoi, K. Akiba, S. Nagatsuka, A. Furusawa, and M. Kozuma  »View Author Affiliations


Optics Express, Vol. 15, Issue 19, pp. 11849-11854 (2007)
http://dx.doi.org/10.1364/OE.15.011849


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Abstract

A probe light in a squeezed vacuum state was injected into cold 87Rb atoms with an intense control light in a coherent state. A sub-MHz window was created due to electromagnetically induced transparency, and the incident squeezed vacuum could pass through the cold atoms without optical loss, as was successfully monitored using a time-domain homodyne method.

© 2007 Optical Society of America

1. Introduction

The coherent transfer of quantum information between light and atoms has been actively investigated, and various methods for its implementation using several phenomena, including the Raman process [1

1. A. E. Kozhekin, K. Mølmer, and E. Polzik, “Quantum memory for light,” Phys. Rev. A 62, 033809/1–5 (2000). [CrossRef]

], quantum non-demolition measurement [2

2. B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurášek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature (London) 432, 482–486 (2004). [CrossRef]

], and electromagnetically induced transparency (EIT) [3

3. M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65, 022314/1–12 (2002). [CrossRef]

, 4

4. D. F. Phillips, A Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001). [CrossRef] [PubMed]

], have been proposed and investigated experimentally. Experimental demonstration of storage and retrieval of a single photon state was first realized using EIT [5

5. T. Chaneliére, 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 (London) 438, 833–836 (2005). [CrossRef]

, 6

6. 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 (London) 438, 837–841 (2005). [CrossRef]

], and this method has attracted a great deal of attention for application to various non-classical lights [7

7. K. Akiba, K. Kashiwagi, T. Yonehara, and M. Kozuma, “Frequency-filtered storage of parametric fluorescence with electromagnetically induced transparency,” Phys. Rev. A 76, 023812/1–5 (2007). [CrossRef]

]. The squeezed vacuum has been an important resource for deterministic intricate quantum information processing. Storing and retrieving the squeezed vacuum state thus enables us to apply such quantum information protocols to the spatially localized atomic ensemble. Furthermore, storage of the squeezed vacuum implies atomic spins being squeezed under the standard quantum limit [8

8. M. Kitagawa and M. Ueda, “Squeezed spin states,” Phys. Rev. A 47, 5138–5143 (1993). [CrossRef] [PubMed]

], which is useful for precise measurements such as magnetometry [9

9. J. Geremia, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Quantum Kalman filtering and the Heisenberg limit in atomic magnetometry,” Phys. Rev. Lett. 91, 250801/1–4 (2003). [CrossRef]

]. The storage and retrieval of light with EIT is based on ultraslow propagation of light by steep dispersion within the transparency window. The group velocity of an incident light pulse can be dramatically reduced by simply narrowing the transparency window. Thus, the establishment of a technique for detecting the squeezed vacuum passed through a narrow transparency window forms the foundation for storage and retrieval of the squeezed vacuum.

The first experimental confirmation of EIT with a squeezed vacuum [10

10. D. Akamatsu, K. Akiba, and M. Kozuma, “Electromagnetically induced transparency with squeezed vacuum,” Phys. Rev. Lett. 92, 203602/1–4 (2004). [CrossRef]

] employed the homodyne detection method with a monochromatic local oscillator (LO), where the homodyne detection signal was analyzed using a spectrum analyzer. Squeezing was observed when the frequency width of the transparency window was relatively large (2.6 MHz). It is noted that the spectrum analyzer measures the power spectrum by mixing the input signal with an electric local oscillator (eLO) and frequency filtering the mixer output (IF). Practically, a tiny amount of the eLO directly couples to the IF port of the mixer and this leakage is detected when the eLO frequency is within the filter bandwidth. Eventually, a sharp peak appears at the low frequency region reflecting the ‘shape of the filter’, which mainly limited the detectable minimum frequency of the squeezing.

In order to solve this problem and realize ultra-slow propagation of a squeezed vacuum, homodyne detection with bichromatic LO having the frequency components of ν0±e was utilized [11

11. 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,” quant-ph/061109 (to appear in Physical Review Letters).

], where n0 and e were the carrier frequency of the squeezed vacuum and the center frequency of the spectrum analyzer, respectively. Since this method is sensitive to the degenerate frequency component (ν0), squeezing was observed within the sub-MHz transparency window and the ultra-slow propagation of a squeezed vacuum pulse was realized. However, the bichromatic homodyne method is also sensitive to the two-mode quadrature noise consisting of ν0±2ε, which are usually present outside the transparency window, since ε has to be set to a relatively high frequency to avoid the specific peak reflecting the ‘shape of the filter’ of the spectrum analyzer. Thus, the observable squeezing level inevitably decreases in the storage and retrieval process.

2. Experiment

Our experimental setup is shown schematically in Fig. 1. We prepared magneto-optically trapped and laser cooled 87Rb atoms and employed them as the EIT medium. One cycle of our experiment was 10 ms. Each cycle consisted of the preparation of cold atoms (9 ms) and the measurement of EIT (1 ms). During the preparation period, the Rb gas was magneto-optically trapped for 5.5 ms, after which the magnetic field was turned off. After the eddy current ceased (~3 ms), both the cooling and repumping lights were turned off and depumping light tuned to F=2→F’=2 transition was made incident on the gas to prepare cold atoms in the F=1 state.

Fig. 1. Schematic diagram of the experimental setup. BS: beam splitter, HBS: half beam splitter, AOM: acousto-optic modulator, PD: photodetector, PZT: piezo electric transducer, Amp.: RF amplifier, Sq. Vac.: squeezed vacuum.

We first evaluated the frequency width of the EIT window with a weak probe light in a coherent state. Ti:Sapphire laser 1 was tuned to 52S1/2, F=1→52P1/2, F’=2, which corresponds to a probe transition. A weak light from this laser was made incident on the OPO cavity, and the output beam was used as a probe light. Note that the probe light was in a coherent state because the second harmonic light in front of the OPO cavity was blocked. The procedure described above enabled us to employ a coherent state of the probe light with a spatial mode that was identical to that of the squeezed vacuum used in the later experiment. Ti:Sapphire laser 2 was tuned to 52S1/2, F=2→52P1/2, F’=2 and was used for the control light. The relative frequency between the probe and the control lights was stabilized with a synthesizer and AOM1 using a feed-forward method [11

11. 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,” quant-ph/061109 (to appear in Physical Review Letters).

, 15

15. M. Kourogi, B. Widiyatmoko, K. Imai, T. Shimizu, and M. Ohtsu, “Accurate relative frequency cancellation between two independent lasers,” Opt. Lett. 24, 16–18 (1999). [CrossRef]

]. During the measurement period, the probe and the control lights were incident on the cold Rb gas with a crossing angle of 2.5°. The power of the control light µW. The waists of the probe and the control lights were 150 µm and 550 µm, respectively. These lights were circularly polarized in the same direction by using quarter waveplates (λ/4). It is noted that the atomic sample prepared here was hyperfine pumped, but unpolarized. Choosing the same circular polarizations for both the probe and the control lights allowed us to keep high transparency while the Zeeman degeneracy of the atomic levels was concerned [5

5. T. Chaneliére, 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 (London) 438, 833–836 (2005). [CrossRef]

]. The probe light that passed through the cold atoms was photon-counted using a silicon avalanche photodiode (Perkin-Elmer: SPCM-AQR). The transmission spectrum obtained by scanning the frequency of the control light is shown in Fig. 2, where the atoms were almost transparent around two-photon resonance, and the half width at half maximum was approximately 300 kHz. The slight asymmetry of the signal originated from the atomic density variation during the measurement time due to thermal diffusion.

Fig. 2. Transmission spectrum of the coherent probe light as a function of the two-photon detuning. Trace (A) indicates transmission spectrum when the probe light was incident on the cold atoms with the control light. Trace (B) shows the spectrum without the control light.

During the measurement period, we imported signals from the homodyne detector into the high-speed digital oscilloscope and performed Fourier transform of the obtained real-time waveforms, where the signal sampling rate was 5×107 samples/sec. Vertical resolution of the digital oscilloscope was 8 bits and thus the dynamic range for the power measurement was almost 50dB. In order to minimize the attribution of the classical noises to the homodyne signal, we adjusted the power balance between the two LO beams as much as possible. We applied classical power modulation to the LO and minimized the modulation signal from the balanced homodyne detector by changing the reflectivity of the half beam splitter, which was carried out by adjusting the angle of the splitter. Eventually we could achieve -58 dB of suppression for the classical modulation. Figure 3(a) indicates the frequency spectrum of the quadrature noise for the squeezed vacuum, where trace (A) indicates the shot noise and traces (B) and (C) indicate the quadrature noises without the cold atoms. Here, the relative phases were set to θ=π/2 and 0, respectively. Each data was averaged over 1,000 times. The sharp peaks in Fig. 3(a) originated from the electric circuit noises of the homodyne detector and thus they could not be eliminated by balancing the laser intensities. The quadrature noise was approximately flat over the frequency range shown in Fig. 3(a) because the spectrum width of the OPO (15 MHz) was much broader than the measurement frequency range (1.5 MHz). Traces (D) and (E) indicate the measured quadrature noise of the squeezed vacuum passed through the cold atoms with the control light, where the relative phase was set to θ=π/2 and 0, respectively. Both anti-squeezing and squeezing were observed within the sub-MHz narrow frequency region, which corresponds to the transparency window caused by EIT.

Fig. 3. (a) Quadrature noise of the probe light in the squeezed state. Trace (A) indicates the shot noise. Traces (B) and (C) show the quadrature noises of the probe light without cold atoms, where the relative phase were θ=π/2 and 0, respectively. Traces (D) and (E) show the quadrature noises when the probe light was incident on the cold atoms with the control light, where the relative phase were θ=π/2 and 0, respectively. (b) The numerically simulated noise spectrum for the squeezed vacuum passed through the cold atoms under the EIT condition. Trace (A) indicates the shot noise. Traces (B) and (C) show the quadrature noises for θ=π/2 and 0, respectively.

X̂(ν,θ)=âν0+νexp(iθ)+âν0νexp(iθ),
(1)

where the sideband frequencies are ν0±ν [17

17. B. Yurke, “Squeezed-coherent-state generation via four–wave mixers and detection via homodyne detectors,” Phys. Rev. A 32, 300–310 (1985) [CrossRef] [PubMed]

]. Now we consider the situation where the opposite sign of the phase shifts ±ϕ are added to the two sidebands,i.e.,

X̂(ν,θ,ϕ)=âν0+νexp(iθ)exp(iϕ)+âν0νexp(iθ)exp(i(ϕ)).
(2)

The quadrature noise is given by

ΔX̂(ν,θ,ϕ)2=(X̂(ν,θ,ϕ)X̂(ν,θ,ϕ))(X̂(ν,θ,ϕ)X̂(ν,θ,ϕ))Sym
=12X̂(ν,θ,ϕ)X̂(ν,θ,ϕ)+X̂(ν,θ,ϕ)X̂(ν,θ,ϕ)X̂(ν,θ,ϕ)X̂(ν,θ,ϕ)
=12X̂(ν,θ)X̂(ν,θ)+X̂(ν,θ)X̂(ν,θ)X̂(ν,θ)X̂(ν,θ)
=ΔX̂(ν,θ)2
(3)

where

ÂB̂Sym=ÂB̂+B̂Â2.
(4)

Namely, additional phase ϕ does not affect the power noise of the quadrature amplitude.

Figure 3(b) shows the numerical simulation of the quadrature noises of the squeezed vacuum that passed through the cold atoms under the EIT condition, where, for the sake of simplicity, we assumed the incident squeezed vacuum experienced the optical loss corresponding to Fig. 2 and the incident anti-squeezing and squeezing levels were constant in all frequency regions. The absorption loss is represented by the model using a beam splitter whose transmittance T(ν) is dependent on the frequency of the light. The quadrature noise of the squeezed vacuum experienced absorption loss is given by

ΔX̂(ν,θ)2=14{T(ν)(cosh2rcos2θsinh2r)+(1T(ν))},
(5)

where r is the squeezing parameter. We use the average of the transmission of the coherent probe light passing through the atoms with the control light whose detuning was ±ν, which is shown in Fig. 2, as T(ν). The numerical simulation is in good agreement with the experimentally obtained noise spectrum.

3. Conclusion

In conclusion, we have succeeded in observing the EIT spectrum of the squeezed vacuum, where both squeezing and anti-squeezing were monitored within sub-MHz transparency window. The observation of squeezing for such a low-frequency region is an essential step in the realization of the storage and retrieval of the squeezed vacuum.

Acknowledgment

The authors would like to thank N. Takei for engaging in numerous helpful discussions. Two of the authors (D. A. and K. A.) were supported by the Japan Society for the Promotion of Science. This study was supported by a Grant-in-Aid for Scientific Research (B) and the 21st Century COE Program at Tokyo Tech, “Nanometer-Scale Quantum Physics” by the MEXT.

References and links

1.

A. E. Kozhekin, K. Mølmer, and E. Polzik, “Quantum memory for light,” Phys. Rev. A 62, 033809/1–5 (2000). [CrossRef]

2.

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurášek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature (London) 432, 482–486 (2004). [CrossRef]

3.

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65, 022314/1–12 (2002). [CrossRef]

4.

D. F. Phillips, A Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001). [CrossRef] [PubMed]

5.

T. Chaneliére, 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 (London) 438, 833–836 (2005). [CrossRef]

6.

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 (London) 438, 837–841 (2005). [CrossRef]

7.

K. Akiba, K. Kashiwagi, T. Yonehara, and M. Kozuma, “Frequency-filtered storage of parametric fluorescence with electromagnetically induced transparency,” Phys. Rev. A 76, 023812/1–5 (2007). [CrossRef]

8.

M. Kitagawa and M. Ueda, “Squeezed spin states,” Phys. Rev. A 47, 5138–5143 (1993). [CrossRef] [PubMed]

9.

J. Geremia, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Quantum Kalman filtering and the Heisenberg limit in atomic magnetometry,” Phys. Rev. Lett. 91, 250801/1–4 (2003). [CrossRef]

10.

D. Akamatsu, K. Akiba, and M. Kozuma, “Electromagnetically induced transparency with squeezed vacuum,” Phys. Rev. Lett. 92, 203602/1–4 (2004). [CrossRef]

11.

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,” quant-ph/061109 (to appear in Physical Review Letters).

12.

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, “Generation of a superposition of odd photon number states for quantum information networks,” Phys. Rev. Lett. 97, 083604/1–4 (2006). [CrossRef]

13.

N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, “Time-gated Einstein-Podolsky-Rosen correlation,” Phys. Rev. A 74, 060101/1–4 (2006). [CrossRef]

14.

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, 2344–2346 (2006) [CrossRef] [PubMed]

15.

M. Kourogi, B. Widiyatmoko, K. Imai, T. Shimizu, and M. Ohtsu, “Accurate relative frequency cancellation between two independent lasers,” Opt. Lett. 24, 16–18 (1999). [CrossRef]

16.

E. S. Polzik, J. Carri, and H. J. Kimble, “Atomic spectroscopy with squeezed light for sensitivity beyond the vacuum-state limit,” Appl. Phys. B 55, 279–290 (1992). [CrossRef]

17.

B. Yurke, “Squeezed-coherent-state generation via four–wave mixers and detection via homodyne detectors,” Phys. Rev. A 32, 300–310 (1985) [CrossRef] [PubMed]

OCIS Codes
(270.0270) Quantum optics : Quantum optics
(270.6570) Quantum optics : Squeezed states

ToC Category:
Quantum Optics

History
Original Manuscript: July 13, 2007
Revised Manuscript: August 27, 2007
Manuscript Accepted: August 29, 2007
Published: September 4, 2007

Citation
M. Arikawa, K. Honda, D. Akamatsu, Y. Yokoil, 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, 11849-11854 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-19-11849


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References

  1. A. E. Kozhekin, K. Mølmer, and E. Polzik, "Quantum memory for light," Phys. Rev. A 62, 033809/1-5 (2000). [CrossRef]
  2. B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurášek, and E. S. Polzik, "Experimental demonstration of quantum memory for light," Nature (London) 432, 482-486 (2004). [CrossRef]
  3. M. Fleischhauer and M. D. Lukin, "Quantum memory for photons: dark-state polaritons," Phys. Rev. A 65, 022314/1-12 (2002). [CrossRef]
  4. D. F. Phillips, A, Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, "Storage of light in atomic vapor," Phys. Rev. Lett. 86, 783-786 (2001). [CrossRef] [PubMed]
  5. T. Chaneliére, 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 (London) 438, 833-836 (2005). [CrossRef]
  6. 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 (London) 438, 837-841 (2005). [CrossRef]
  7. K. Akiba, K. Kashiwagi, T. Yonehara, and M. Kozuma, "Frequency-filtered storage of parametric fluorescence with electromagnetically induced transparency," Phys. Rev. A 76, 023812/1-5 (2007). [CrossRef]
  8. M. Kitagawa, and M. Ueda, "Squeezed spin states," Phys. Rev. A 47, 5138-5143 (1993). [CrossRef] [PubMed]
  9. J. Geremia, J. K. Stockton, A. C. Doherty, and H. Mabuchi, "Quantum Kalman filtering and the Heisenberg limit in atomic magnetometry," Phys. Rev. Lett. 91, 250801/1-4 (2003). [CrossRef]
  10. D. Akamatsu, K. Akiba, and M. Kozuma, "Electromagnetically induced transparency with squeezed vacuum," Phys. Rev. Lett. 92, 203602/1-4 (2004). [CrossRef]
  11. 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," quant-ph/061109 (to appear in Physical Review Letters).
  12. J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, "Generation of a superposition of odd photon number states for quantum information networks," Phys. Rev. Lett. 97, 083604/1-4 (2006). [CrossRef]
  13. N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, "Time-gated Einstein-Podolsky-Rosen correlation," Phys. Rev. A 74, 060101/1-4 (2006). [CrossRef]
  14. 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, 2344-2346 (2006). [CrossRef] [PubMed]
  15. M. Kourogi, B. Widiyatmoko, K. Imai, T. Shimizu, and M. Ohtsu, "Accurate relative frequency cancellation between two independent lasers," Opt. Lett. 24, 16-18 (1999). [CrossRef]
  16. E. S. Polzik, J. Carri, and H. J. Kimble, "Atomic spectroscopy with squeezed light for sensitivity beyond the vacuum-state limit," Appl. Phys. B 55, 279-290 (1992). [CrossRef]
  17. B. Yurke, "Squeezed-coherent-state generation via four-wave mixers and detection via homodyne detectors," Phys. Rev. A 32, 300-310 (1985). [CrossRef] [PubMed]

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