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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 5 — Feb. 28, 2011
  • pp: 4113–4120
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Phase-controlled switching by interference between incoherent fields in a double-Λ system

Hoonsoo Kang, Bongjune Kim, Young Ho Park, Cha-Hwan Oh, and In Won Lee  »View Author Affiliations


Optics Express, Vol. 19, Issue 5, pp. 4113-4120 (2011)
http://dx.doi.org/10.1364/OE.19.004113


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Abstract

We showed experimentally interference could be occurred between incoherent lights in a double-Λ lambda transition implemented with rubidium atomic vapor. Switching of probe transmission was controlled by the phases of two` independent probe lasers with low light intensity. More than 70% of the probe transmission could be switched by ultra-weak incoherent field. We suggested optically cryptic information could be delivered by the phase-controlled switching with incoherent fields in a double-Λ system.

© 2011 OSA

1. Introduction

A double-Λ EIT system has attracted much attention because it has many applications to coherent optical manipulations. Pulse matching in two modes, three-level double lambda system was studied theoretically to show that two mode group velocities could be matched by controllable four wave mixing channel [12

12. L. Deng and M. G. Payne, “Achieving induced transparency with one- and three-photon destructive interference in a two-mode, three-level, double-Λ system,” Phys. Rev. A 71(1), 011803 (2005) (R). [CrossRef]

]. It was noted that the transparency induced in double lambda system is not collaborating with dark state which is eigenstate decoupled to optical transition in conventional EIT system. Formation and propagation of matched and coupled ultraslow optical soliton pairs was considered in four-level double lambda system. Phase-controlled switching effect was demonstrated experimentally in double lambda four-level system implemented by gaseous Rb atom [13

13. H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Phase-controlled light switching at low light levels,” Phys. Rev. A 73(1), 011802 (2006) (R). [CrossRef]

]. The switching effect was more accurately observed with ultra-weak probe intensity as several tens of photon [14

14. J. Zhang, G. Hernandez, and Y. Zhu, “All-optical switching at ultralow light levels,” Opt. Lett. 32(10), 1317–1319 (2007). [CrossRef] [PubMed]

].

Georgiades et al. observed quantum interference of two-photon transitions in cold atoms [15

15. N. Ph. Georgiades, E. S. Polzik, and H. J. Kimble, “Frequency metrology by use of quantum interference,” Opt. Lett. 21(20), 1688–1690 (1996). [CrossRef] [PubMed]

]. Korsunsky et al. studied the phase-dependent coherent population trapping [16

16. E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, “Phase-dependent electromagnetically induced transparency,” Phys. Rev. A 59(3), 2302–2305 (1999). [CrossRef]

]. Huss et al. observed the correlation of the phase fluctuation in a double-Λ system [17

17. A. F. Huss, R. Lammegger, C. Neureiter, E. A. Korsunsky, and L. Windholz, “Phase correlation of laser waves with arbitrary frequency spacing,” Phys. Rev. Lett. 93(22), 223601 (2004). [CrossRef] [PubMed]

]. Recently, the phase-controlled switching has been implemented with biexcitonic double-Λ system of semiconductor quantum well structure [18

18. H. Kang, Y. Park, I. Sohn, and M. Jeong, “All-optical switching with a biexcitonic double lambda system,” Opt. Commun. in press.

]. Meanwhile, the generation of correlated single photon pair has been studied by using Raman scattering followed by four-wave mixing in double lambda four-level system [19

19. P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: use of a single driving laser,” Phys. Rev. Lett. 97(11), 113602 (2006). [CrossRef] [PubMed]

].

We define the relevant Rabi frequency as Ωmn=μmnEmn(t)/, where μmn is the dipole transition matrix element. The coupling field drives the transition |F=3,   mF=+1|F=2,   mF=+2   (|F=3,   mF=+2) with the Rabi frequency ΩC1(ΩC2). Two weak probe fields drive |F=3,   mF=+3|F=2,   mF=+2 and |F=3,   mF=+3|F=3,   mF=+2 with Rabi frequencies, ΩP1 and ΩP2 respectively. Here, Ωmn=|Ωmn|eiϕmn is characterized by the amplitude |Ωmn| and phase ϕmn. For |ΩC1||ΩC2|, |ΩP1||ΩP2| and |ΩC1|>>|ΩP1|, the excitation in double lambda system can be divided into two excitation paths because the interference supported by four-wave mixing process is occurred in a double-Λ system [12

12. L. Deng and M. G. Payne, “Achieving induced transparency with one- and three-photon destructive interference in a two-mode, three-level, double-Λ system,” Phys. Rev. A 71(1), 011803 (2005) (R). [CrossRef]

]:

|F=3,   mF=+3|F=2,   mF=+2 and |F=3,   mF=+3|F=3,   mF=+2|F=3,   mF=+1|F=2,   mF=+2equivalently, |F=3,   mF=+3|F=3,   mF=+2and|F=3,   mF=+3|F=2,   mF=+2|F=3,   mF=+1|F=3,   mF=+2).

When the interference of two excitation path is destructive with the condition, ΩP1/ΩP2=ΩC1/ΩC2 as described in Ref 12

12. L. Deng and M. G. Payne, “Achieving induced transparency with one- and three-photon destructive interference in a two-mode, three-level, double-Λ system,” Phys. Rev. A 71(1), 011803 (2005) (R). [CrossRef]

, excitation does not occur and both probe fields propagate in the medium without attenuation. When ΩP1/ΩP2=ΩC1/ΩC2, the interference is constructive and both probe fields are attenuated. Destructive interference is switched with the constructive interference by changing the phase of the optical fields. If the coupling and probe fields, ΩC1 and ΩP 1 are split from one laser source, these are coherent each other and have same arbitrary phase which comes from the laser source. This arbitrary phase would be cancelled out in four-wave mixing process:

|F=3,   mF=+3|F=2,   mF=+2|F=3,   mF=+1|F=3,   mF=+2|F=3,   mF=+3.

The first two-photon process in the transition is a probe-coupling stimulated Raman scattering which cancels the arbitrary phase imposed by the laser source. The other pair of coupling and probe fields, ΩC2 and ΩP 2 is split by the other independent laser source. The arbitrary phase imposed by the other laser source could be removed by two-photon process in four-wave mixing transition. The phase dependent switch can be controlled just by the external optical phase delay of the coupling and probe fields. Two probe fields, ΩP 1 and ΩP 2 generated by two independent laser systems could interfere each other because the transmission of probe field could be phase-dependent upon the relative phase difference between two probe fields. In section 2, it will be shown the interference between two independent probe fields experimentally. To show the possibility of the application of the incoherent interference to phase-controlled switching device, optical information was encrypted in the phase of probe field and it could be decrypted by phase-controlled switching in double-Λ system.

2. Experiment

A double-Λ system was implemented with Zeeman levels of Rb85 D1 transition (Fig. 1). Each coupling(ΩC1,2).-probe (ΩP1,2) transitions were excited with the opposite circular polarizations. We employed two independent ECDL (External Cavity Diode Laser) resonant on Rb85 D1 transition. Each ECDL was split to coupling-probe field pair and PZT (piezoelectric transducer) was employed to induce the phase modulation of probe field by changing the optical path (Fig. 2
Fig. 2 Experimental setup. Photo diode (PD) and polarization maintenance optical fibre (PMOF).
). Two probe (coupling) fields were coupled to a polarization maintenance optical fibre for the easiness of collinear spatial mode matching. Rb85 atom gaseous cell with nitrogen buffer gas was shield with 3-layer μ-metal to remove geomagnetic field. The Rb85 vapor cell was heated to 60° Celsius and wound by copper wire to generated static magnetic field of the parallel direction with the coupling-probe laser propagation. The population of F=2 ground hyperfine state was optically pumped to mF=3 Zeeman sublevel by two coupling fields (Fig. 1). A repump laser was used to excite Rb85 D2 transition from F=3 ground hyperfine state to compensate the population to F=2 state, which is not shown in Fig. 2.

To observe two-photon resonance in each Λ system with coupling-probe transition, the transmission of one probe field was measured by photo diode, (PD1 in Fig. 2) with scanning the static magnetic field applied to Rb vapour cell. The static magnetic field induces Zeeman splitting which detunes two-photon resonance from the frequency of the coupling and probe fields. When ECDL are frequency-locked on one-photon resonance of Rb D1 transition, two-photon resonance could be observed to be typical EIT. The amplitude of both coupling Rabi frequencies, |ΩC1| and |ΩC2| were adjusted same to be 150×2π kHz and those of both probe field, |ΩP1| and |ΩP2| were adjusted to be |ΩP1||ΩP2||ΩC1|/100 to satisfy the destructive interference condition of double-Λ system. We directly measured the power of coupling and probe beams and estimated the probe Rabi frequency by comparing with the coupling Rabi frequency. The coupling beam power was about several mW and that of probe was sub-μW with similar beam size. Our photo-detector was sensitive enough to observe this range of power. Interference of double-Λ system could be controlled by the phase of coupling and probe fields. PZT attached on the mirror changed the optical path of the probe fields, which changed the phase of probe field in double-Λ transition. The transmission of both probe fields was shown with the probe phase difference ϕP1ϕP2 for the destructive interference (0), an intermediate interference (π/2) and the constructive interference (π) in Fig. 3
Fig. 3 The blue line is the transmission of the probe fields when destructive interference (ϕP1ϕP2=0) is occurred in a double-Λ system, the red line is that of the probe fields when ϕP1ϕP2=π/2 and the black line is when constructive interference is occurred (ϕP1ϕP2=π).
. PZT3 was adjusted to have the relative phase 0 between the coupling fields.

Random noise can be loaded on the phase of both probe fields while transforming target information through a double-Λ system. This might be applied to optical information transformation with incoherent lights carrying additional random noise to conceal target optical information. Only relative phase difference between incoherent probe fields could control the transmission of the probe fields while the phase difference between coupling fields fixed. Figure 4(a)
Fig. 4 (a) The phase shift of probe 1 driven by PZT1 in time sequence. (b) The phase shift of probe 2 driven by PZT2. (c) The relative phase difference between the probe fields (d) The transmission signal of the probe fields while the relative phase of the coupling fields was fixed to π. The transmission value of 100% is accord to the maximal value of the blue curve of Fig. 3. (e) The transmission signal of the probe fields while the relative phase of the coupling fields was fixed to 0.
shows the phase shift of Probe 1, ϕP1 by PZT1 in time sequence. Figure 4(b) shows the phase shift of Probe 2, ϕP2 by PZT2. Those might transfer target information with random noise which could be added for encryption. The relative phase difference between Fig. 4(a) and 4(b) controls the probe transmission to decrypt the target information. Figure 4(c) shows the target information which is the relative phase difference between Probe 1 and 2. Figure 4(d) shows the transmission of the probe fields after interacting in a double-Λ system while the relative phase of the coupling fields was fixed to π by PZT3. Photo detector, PD2 in Fig. 2 could not observe any interference fringe. It is impossible to recover the target information without a double-Λ system because the probe fields are incoherent not to be interfered each other. The interference pattern of the transmission could be changed with the relative phase of the coupling fields either. Figure 4(e) shows the transmission of the probe fields with the relative phase of coupling fields fixed to 0 which inverts the transmission curve.

Schematics of encrypt optical information with incoherent light phase-controlled switching is shown in Fig. 5
Fig. 5 The schematics of encrypt optical information transportation with incoherent light phase-controlled switching.
. There are two parts for transforming encrypted optical information. One of them is Encoder which encrypts target information on two probe fields. The other part is Decoder which decrypts the encrypted optical information. At first, Decoder sends random noised two probe fields, Probe 1 and 2 through free space or optical fiber to Encoder. Then Encoder modulates optical phase of two incoherent probe fields to encrypt the target information with adding random noise on both probe fields as conducted in Fig. 4. The modulated probe fields, Probe 1* and 2* are delivered back to Decoder who will decrypt the target information in a double-Λ system. Decoder should prepare laser sources and atomic material to implement a double-Λ system while Encoder needs to have optical phase shifter. Eavesdropping is nearly impossible because interference between probe fields cannot be observed without the original double-Λ system. Eavesdropper might wiretap by interfering each probe signals of before and after Encoder’s encryption to read the modulate pattern on each probe fields. This eavesdropping might be even difficult to prepare right optical delay in reality because Encoder station has various delay process sending stream of optical signals. Furthermore, there might be a key code of the random relative phase difference between coupling fields which could be shared between Encoder and Decoder before encrypt information transformation. Coherence length of laser sources for coupling-probe field is critical factor for long range information transformation with a double-Λ system. Our laser source has about 200 m coherence length but it is feasible in modern technology to increase coherence length to more than 10,000 times with frequency stabilized laser source with high finesse cavity. We can consider the encrypt information transformation between earth stations via satellite (Fig. 6
Fig. 6 The schematics of the encrypt information transformation between earth stations via satellite.
). The satellite needs to be equipped with telescope to receive and send optical signal from earth stations. Decoder station is equipped with a telescope, long coherence length laser system and a double-Λ system. Decoder sends random noised probe fields to satellite which receive the optical signal and send to Encoder station. Encoder encrypts target information on probe fields with random noise. The optical information is send back to Decoder via the satellite. We expect encrypt optical information transformation can be realized between multi-site earth stations to cover the whole planet.

3. Conclusion

Acknowledgement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0013310) and partly Asian Laser Center Program through a grant provided by the Gwangju Institute of Science & Technology.

References and links

1.

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today 50(7), 36 (1997). [CrossRef]

2.

J. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in Coherent Media,” Rev. Mod. Phys. 77(2), 633–673 (2005). [CrossRef]

3.

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(6720), 594–598 (1999). [CrossRef]

4.

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today 50(7), 36 (1997). [CrossRef]

5.

H. Schmidt and A. Imamogdlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21(23), 1936–1938 (1996). [CrossRef] [PubMed]

6.

S. E. Harris and Y. Yamamoto, “Photon Switching by Quantum Interference,” Phys. Rev. Lett. 81(17), 3611–3614 (1998). [CrossRef]

7.

H. Kang and Y. Zhu, “Observation of Large Kerr Nonlinearity at Low Light Intensities,” Phys. Rev. Lett. 91(9), 093601 (2003). [CrossRef] [PubMed]

8.

M. D. Lukin, “Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75(2), 457–472 (2003). [CrossRef]

9.

M. D. Eisaman, L. Childress, A. André, F. Massou, A. S. Zibrov, and M. D. Lukin, “Shaping quantum pulses of light via coherent atomic memory,” Phys. Rev. Lett. 93(23), 233602 (2004). [CrossRef] [PubMed]

10.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90(19), 197902 (2003). [CrossRef] [PubMed]

11.

Z.-B. Wang, K.-P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in 87Rb,” Phys. Rev. Lett. 97(6), 063901 (2006). [CrossRef] [PubMed]

12.

L. Deng and M. G. Payne, “Achieving induced transparency with one- and three-photon destructive interference in a two-mode, three-level, double-Λ system,” Phys. Rev. A 71(1), 011803 (2005) (R). [CrossRef]

13.

H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Phase-controlled light switching at low light levels,” Phys. Rev. A 73(1), 011802 (2006) (R). [CrossRef]

14.

J. Zhang, G. Hernandez, and Y. Zhu, “All-optical switching at ultralow light levels,” Opt. Lett. 32(10), 1317–1319 (2007). [CrossRef] [PubMed]

15.

N. Ph. Georgiades, E. S. Polzik, and H. J. Kimble, “Frequency metrology by use of quantum interference,” Opt. Lett. 21(20), 1688–1690 (1996). [CrossRef] [PubMed]

16.

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, “Phase-dependent electromagnetically induced transparency,” Phys. Rev. A 59(3), 2302–2305 (1999). [CrossRef]

17.

A. F. Huss, R. Lammegger, C. Neureiter, E. A. Korsunsky, and L. Windholz, “Phase correlation of laser waves with arbitrary frequency spacing,” Phys. Rev. Lett. 93(22), 223601 (2004). [CrossRef] [PubMed]

18.

H. Kang, Y. Park, I. Sohn, and M. Jeong, “All-optical switching with a biexcitonic double lambda system,” Opt. Commun. in press.

19.

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: use of a single driving laser,” Phys. Rev. Lett. 97(11), 113602 (2006). [CrossRef] [PubMed]

OCIS Codes
(020.4180) Atomic and molecular physics : Multiphoton processes
(060.1660) Fiber optics and optical communications : Coherent communications

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: December 8, 2010
Revised Manuscript: January 15, 2011
Manuscript Accepted: February 9, 2011
Published: February 16, 2011

Citation
Hoonsoo Kang, Bongjune Kim, Young Ho Park, Cha-Hwan Oh, and In Won Lee, "Phase-controlled switching by interference between incoherent fields in a double-Λ system," Opt. Express 19, 4113-4120 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-5-4113


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References

  1. S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today 50(7), 36 (1997). [CrossRef]
  2. J. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in Coherent Media,” Rev. Mod. Phys. 77(2), 633–673 (2005). [CrossRef]
  3. 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(6720), 594–598 (1999). [CrossRef]
  4. S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today 50(7), 36 (1997). [CrossRef]
  5. H. Schmidt and A. Imamogdlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21(23), 1936–1938 (1996). [CrossRef] [PubMed]
  6. S. E. Harris and Y. Yamamoto, “Photon Switching by Quantum Interference,” Phys. Rev. Lett. 81(17), 3611–3614 (1998). [CrossRef]
  7. H. Kang and Y. Zhu, “Observation of Large Kerr Nonlinearity at Low Light Intensities,” Phys. Rev. Lett. 91(9), 093601 (2003). [CrossRef] [PubMed]
  8. M. D. Lukin, “Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75(2), 457–472 (2003). [CrossRef]
  9. M. D. Eisaman, L. Childress, A. André, F. Massou, A. S. Zibrov, and M. D. Lukin, “Shaping quantum pulses of light via coherent atomic memory,” Phys. Rev. Lett. 93(23), 233602 (2004). [CrossRef] [PubMed]
  10. C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90(19), 197902 (2003). [CrossRef] [PubMed]
  11. Z.-B. Wang, K.-P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in 87Rb,” Phys. Rev. Lett. 97(6), 063901 (2006). [CrossRef] [PubMed]
  12. L. Deng and M. G. Payne, “Achieving induced transparency with one- and three-photon destructive interference in a two-mode, three-level, double-Λ system,” Phys. Rev. A 71(1), 011803 (2005) (R). [CrossRef]
  13. H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Phase-controlled light switching at low light levels,” Phys. Rev. A 73(1), 011802 (2006) (R). [CrossRef]
  14. J. Zhang, G. Hernandez, and Y. Zhu, “All-optical switching at ultralow light levels,” Opt. Lett. 32(10), 1317–1319 (2007). [CrossRef] [PubMed]
  15. N. Ph. Georgiades, E. S. Polzik, and H. J. Kimble, “Frequency metrology by use of quantum interference,” Opt. Lett. 21(20), 1688–1690 (1996). [CrossRef] [PubMed]
  16. E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, “Phase-dependent electromagnetically induced transparency,” Phys. Rev. A 59(3), 2302–2305 (1999). [CrossRef]
  17. A. F. Huss, R. Lammegger, C. Neureiter, E. A. Korsunsky, and L. Windholz, “Phase correlation of laser waves with arbitrary frequency spacing,” Phys. Rev. Lett. 93(22), 223601 (2004). [CrossRef] [PubMed]
  18. H. Kang, Y. Park, I. Sohn, and M. Jeong, “All-optical switching with a biexcitonic double lambda system,” Opt. Commun. in press.
  19. P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: use of a single driving laser,” Phys. Rev. Lett. 97(11), 113602 (2006). [CrossRef] [PubMed]

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