Thulium doped crystals for quantum information storage

ARTICLE IN PRESS Journal of Luminescence 129 (2009) 1951–1954

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Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin

Thulium doped crystals for quantum information storage R. Lauro , J. Ruggiero, A. Louchet, A. Alexander, T. Chanelie`re, I. Lorgere´, F. Bretenaker, F. Goldfarb, J.-L. Le Goue¨t ˆtiment 505, 91405 Orsay cedex, France ´ Cotton, CNRS-UPR 3321, Univ Paris Sud, Ba Laboratoire Aime

a r t i c l e in fo

abstract

Available online 5 April 2009

Optically driving nuclear spin waves in a Tm:YAG crystal, we experimentally demonstrate the feasibility of a three-level L system in this material, which is a foundation step in the prospect of quantum memory investigations. Varying the spin state splitting with an external magnetic field, we show that the nuclear spin coherence lifetime remains close to 350 ms over a wide range of variation of this splitting. Finally, we demonstrate fast coherent population transfer between the spin states. & 2009 Elsevier B.V. All rights reserved.

Keywords: Rare earth ions Thulium Coherent transients Raman echo Stimulated Raman adiabatic passage Quantum memory

1. Introduction The prospect of practical applications renewed the interest in quantum physics quite recently. The quantum principles led to quantum information growth in the 1990s. For example, Shor found a quantum algorithm which allows large number factorization much faster than classical algorithm, and quantum cryptography [1] appeared as an ideal solution for secret information transport. In a quantum information network, information storage is important. For example, it would be necessary to store and release distant entangled states, or store the result of a quantum operation for a further analysis. A lot of physical systems can be considered. Here, we present a contribution to solid state quantum memories, specifically rare earth ions doped crystals (REIC).

2. Quantum memories Quantum information is related to noise. When the fluctuations of a classical light source are reduced to the quantum limit, noise is equally distributed over a pair of conjugated observables such as photon number and phase, Stokes vector components or field quadratures. A light beam carries quantum information if the noise affecting one observable is squeezed under the standard quantum limit corresponding to equipartition of noise. Of course noise reduction on one observable entails increased noise on the conjugate quantity. Naively speaking, a quantum memory should  Corresponding author. Tel.: +33 1 69 35 20 37.

E-mail address: [email protected] (R. Lauro). 0022-2313/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2009.03.025

be able to restore a signal in the tiniest details, beyond the quantum limit. Resonant excitation of an atomic transition provides appropriate strong coupling between light and matter. We also need to interrogate the memory at will, controlling the moment when the signal is restored. This can be achieved through an auxiliary optical transition, coupled to the quantum field capture transition. Several protocols rely on the L three-level system (Fig. 1). A common upper level links the two transitions that are connected to two sub-levels of the electronic ground state. One transition is used for the quantum capture, the other one serves for the control. They are connected in a very simple way through the common upper level. An additional benefit of this scheme is that the optical coherence that is built by the incoming signal can be converted into a ground state coherence that is immune to relaxation by spontaneous emission. So far, quantum storage has been demonstrated in ultracold atoms [2] and in atomic vapors [3]. To extend these results to solid state media, rare earth ions doped crystals are attractive since they offer very long optical and Raman coherence lifetimes. Moreover, atoms being static, there is no diffusion in these systems. REIC have been subject of a lot of studies for almost 30 years, in the field of coherent transient-based signal-processing schemes [4–7], and are today a promising material for quantum memories [8]. We review some properties of Tm ion, and some experiments which allow optical control of a Raman coherence.

3. Building a multilevel system in Tm:YAG Rare earth ions are well known by spectroscopists for the sharpness of their spectral lines. This property is linked to their long optical coherence lifetime. At low temperature, coherence

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R. Lauro et al. / Journal of Luminescence 129 (2009) 1951–1954

3

B≠0

B=0

4 Control field

3H

Δe

4(0)

3

Signal

2 1

793 nm

Raman coherence

Fig. 1. (Color online) The L interaction scheme. The two optical transitions are coupled to signal field and control field. Optical coherence created by signal field is converted into a Raman coherence thanks to control field, and vice versa.

2 3

Δg

H6(0)

1 relaxation is dominated by spin–spin interactions, a process that is reduced in the so-called non-Kramers ions, exhibiting an even number of 4f electrons. Among non-Kramers ions, trivalent thulium ion offers an optical transition near 800 nm, where diode lasers are available, whereas Pr and Er, two other rare earth ions doped crystals, require dye laser. Excitation source must be stabilized: with our setup we can easily reach sub-kHz linewidth [9], which is a challenging task for dye lasers, because of the high frequency noise generated by the dye jet. We aim at creating a L system in Tm. Although Tm ion has an I ¼ 12 nuclear spin, it does not exhibit hyperfine structure, because of J quenching. Using an external magnetic field, we can lift the degeneracy. However, if the magnetic field induces only a nuclear Zeeman effect, the electronic levels split into mI ¼ 12 and 12 spin sub-levels. Then, we have only two two-level systems, since an optical excitation cannot flip nuclear spin. Fortunately, the coupling between hyperfine interaction and electronic Zeeman effect mixes nuclear spin states. The resulting gyromagnetic tensor is strongly anisotropic, and this anisotropy is different in ground and excited states [10], which means that an appropriate orientation of the magnetic field leads to comparable transition strengths for the two legs of the L system. We can define the branching ratio R of the transition probabilities along the two legs of the L system. Magnetic field is oriented in such a way that branching ratio is optimized, with a value of 0.13 [11]. Hole burning spectroscopy allows us to measure nuclear Zeeman sensitivity. We find Dg =B ¼ 36 MHz=T and De =B ¼ 16 MHz=T.

4. Raman echoes To optically study nuclear spin coherence, and measure nuclear spin superposition lifetime T 2 , we create a spin coherence by optical means. We use a L system connecting the two ground states and one of the exciting state. Initially, atoms are optically pumped into a single sub-level. Spin coherence is created with a bichromatic pulse, whose frequency components o1 and o2 are tuned to optical transitions, but are separated by ground state splitting Dg to achieve the two photon resonance condition. After bichromatic excitation, interactions with environment destroy spin coherence. Still with optical means, we want to probe spin evolution. A solution is to apply a pulse at frequency o1 which excites spin coherence, and create an optical coherence along the other transition of the L system: this is the coherent forward Raman scattering. The resulting optical emission beats with the optical excitation at beat note Dg . We can monitor spin decoherence if we vary the delay between bichromatic pulse and probe pulse (Fig. 3).

Fig. 2. (Color online) Four-level structure in Tm3þ : YAG with an external magnetic field.

light intensity

ω1

time Δg

ω2

light frequency

Δe t12

t12

Fig. 3. (Color online) Raman echo sequence. Frequency o1 corresponds to transition between states 2 and 3, o2 is for transition between 1 and 3. The second pulse fields are optically detuned from the first pulse, while preserving two-photon resonance (see Fig. 2).

However, the ground state splitting is not the same for all atoms. Due to this inhomogeneous broadening, each atom has its own evolution rate, and makes beatnote vanish on timescale of the excitation pulse duration. To compensate this inhomogeneous dephasing, we use a Raman echo procedure [12,13]. After a delay t12 , we send another bichromatic pulse, still fulfilling the two photon resonance condition (see Fig. 3), which reverses spin coherence evolution. After a delay 2  t12, coherences rephase together. If both bichromatic pulses have the same frequencies, two pulses photon echo appears at frequency o1 and o2 . That is why the second bichromatic pulse is detuned optically [14]. Raman echo experiment allows to measure Raman coherence lifetime T 2 . The Raman signal decays with t 12 as e2t12 =T 2 . In Fig. 4, Raman signal is shown for a ground state splitting Dg ¼ 41 MHz. We varied the magnetic field value, hence, ground state splitting, and measured coherence lifetime. Over an 80 MHz range, the spin coherence lifetime seems to be independent of the magnetic field value. We found 350 ms for ground state (Fig. 5).

5. Stimulated Raman adiabatic passage In order to implement a quantum memory, we need to manipulate and prepare atomic populations. For example, in a L three-level system, we could put atoms within a spectral range in

ARTICLE IN PRESS R. Lauro et al. / Journal of Luminescence 129 (2009) 1951–1954

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3 Intensity

Transmitted intensity FFT

Pump

Stokes

2

(μ

400

s)

200

1 Fig. 6. (Color online) L interaction scheme used for STIRAP. Pulse sequence is described. In this experiment, atoms are initially in state 1 and Stokes pulse is applied first.

35

40 Frequency (MHz)

800

2

x

t1

2

600

time

45

Raman coherence lifetime T2 (µs)

Fig. 4. (Color online) For a ground state splitting of 41 MHz, Raman echo signal. Delay time t 12 is varied between 100 and 800 ms.

500 400 300 200 100 0 0

20 40 60 80 Ground state sublevel splitting Δg (MHz)

100

Fig. 5. (Color online) Coherence lifetime T 2 for ground state splittings varying from 3 to 84 MHz.

one of the ground state, and atoms out of this range in the other ground state. Optical pumping could be a solution, but this is an incoherent process, which means it takes a long time, typically much longer than excited state lifetime. In Tm3þ : YAG an efficient optical pumping takes several tens of ms. A coherent process may be used to reduce the preparation time of the atoms. Consider the L system where one of the optical transitions is coupled to a pump pulse and the other one is coupled to a Stokes pulse (see Fig. 6). The three instantaneous eigenvectors depend on both pump and Stokes Rabi frequencies. Rabi frequency determines the strength of the coupling, and is defined as Oi ¼ l:Ei , l being the dipolar momentum and Ei the electric field. Among the three eigenvectors, one is of particular interest (see Eq. (1)). jDi ¼ cosðyÞj1i  sinðyÞj2i tanðyÞ ¼

OP OS

(1) (2)

This is a superposition of ground states 1 and 2, that is not coupled to the excited state: that is why it is called dark state [15]. We can link dark state to processes such as CPT or EIT [16,17]. This state can be optically driven, since mixing angle y is defined by both pump and Stokes Rabi frequencies (see Eq. (2)). There are two interesting situations. When the Stokes field is much larger than the pump field, mixing angle is zero, then dark state

Fig. 7. (Color online) STIRAP experiment. Delay between Stokes and pump fields is varied from 40 to 40 ms.

corresponds to state 1. When the pump is much larger, dark state corresponds to state 2. In an adiabatic evolution [18], atoms stay in the dark state all along the process. This can be achieved thanks to a particular pulse sequence, called counter-intuitive (see Fig. 6). This is the principle of stimulated Raman adiabatic transfer [19], which has been demonstrated very recently in a solid [20]. In experiments, pulses with Gaussian temporal shape, with a full width at half maximum of 20 ms, were used. The delay between two pulses is defined as follows: if Stokes pulse is applied first, delay is negative, and we achieve STIRAP, but if pump field is applied first, delay is positive, and this is bright-STIRAP (see Fig. 7). Initially, all atoms are prepared in state 1 with optical pumping. Delay between the two pulses varied from 40 to 40 ms. For negative delays, transfer efficiency reaches 90%. Efficiency is higher than 50% over a delay range of 20 ms, which corresponds to pulse duration. For very low delays, efficiency is zero. In this case, Stokes pulse has no consequence since it couples empty levels, and is turned off before pump is applied. We should only see optical pumping due to pump pulse, but we probe system too early to see any change in final state population. For positive delays, efficiency is less than 40%. In this case, initial state is not the dark one. During interaction, there are oscillations between ground states and excited state. Then system suffers relaxation. Red curve shows numerical results from optical Bloch equations. For positive delays, oscillations are due to pulse overlapping. Finally, STIRAP is a good way to achieve a near 100% transfer between two ground states. This transfer is done in a very short

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time, much shorter than optical pumping. And this is a more robust process than Pi pulses process for example, because of pulse deformation.

6. Conclusion Thanks to an external magnetic field, a Tm3þ :YAG crystal exhibits a four-level structure, which allows to implement protocols such as electromagnetically induced transparency [8]. An optical control of a Raman was also demonstrated for thulium, using a L interaction scheme, in a Raman echo experiment. In this experiment, the photon echo was eliminated by detuning the two frequencies of bichromatic rephasing pulse. The spin coherence lifetime was measured to be 350 ms, over a 80 MHz ground splitting range. Hence Tm:YAG could be an interesting candidate for quantum memory investigation. With regard to other explored systems such as Pr:YSO, Tm exhibits a similar spin coherence lifetime [21] with a broader and adjustable ground state splitting, allowing for broader bandwidth operation. An STIRAP experiment was described. This experiment allows very fast transfer of population between hyperfine states. We are able to transfer nearly 90% in less than 40 ms, and show efficient optical control of a Raman coherence.

References [1] N. Gisin, G. Ribordy, W. Tittel, H. Zinbden, Rev. Mod. Phys. 74 (2002) 145. [2] T. Chanelie`re, D.N. Matsukevitch, S.D. Jenkins, S.Y. Lan, T.A. Kennedy, A. Kuzmich, Nature (London) 423 (2003) 731. [3] B. Julsgaard, A. Kozhekin, E.S. Polzik, Nature (London) 413 (2001) 400. [4] K.D. Merkel, W.R. Babbitt, Opt. Lett. 23 (1998) 528. [5] H. Lin, T. Wang, T.W. Mossberg, Opt. Lett. 20 (1995) 1658. [6] V. Lavielle, I. Lorgere´, J.-L. Le Goue¨t, S. Tonda, D. Dolfi, Opt. Lett. 28 (2003) 384. [7] G. Gorju, V. Crozatier, I. Lorgere´, J.-L. Le Goue¨t, F. Bretenaker, IEEE Photon. Technol. Lett. 17 (2005) 2385. [8] A.V. Turukhin, V.S. Sudarshanam, M.S. Shahriar, J.A. Musser, B.S. Ham, P.R. Hemmer, Phys. Rev. Lett. 88 (2002) 023602. [9] V. Crozatier, F. de Seze, L. Haals, F. Bretenaker, I. Lorgere´, J.-L. Le Goue¨t, Opt. Comm. 241 (2004) 203. [10] F. de Seze, A. Louchet, V. Crozatier, I. Lorgere´, F. Bretenaker, J.-L. Le Goue¨t, O. Guillot-Noe¨l, Ph. Goldner, Phys. Rev. B 73 (2006) 085112. [11] A. Louchet, J.S. Habib, V. Crozatier, I. Lorgere´, F. Goldfarb, F. Bretenaker, J.-L. Le Goue¨t, O. Guillot-Noe¨l, Ph. Goldner, Phys. Rev. B 75 (2007) 035131. [12] S.R. Hartmann, IEEE J. Quantum Electron. 4 (1968) 802. [13] B.S. Ham, M.S. Shahriar, M.K. Kim, P.R. Hemmer, Phys. Rev. B 58 (1998) 11825. [14] A. Louchet, Y. Le Du, F. Bretenaker, T. Chanelie`re, F. Goldfarb, I. Lorgere´, J.-L. Le Goue¨t, Phys. Rev. B 77 (2008) 195110. [15] M.P. Fewell, B.W. Shore, K. Bergmann, Austal. J. Phys. 50 (1997) 281. [16] H.R. Gray, R.M. Whiteley, C.R. Stround Jr., Opt. Lett. 3 (1978) 218. [17] M. Fleischhauer, M.D. Lukin, Phys. Rev. Lett. 84 (2000) 5094. [18] J.R. Kuklinski, U. Gaubatz, F.T. Hioe, K. Bergmann, Phys. Rev. A 40 (1989) 6741. [19] K. Bergmann, H. Theuer, B.W. Shore, Rev. Mod. Phys. 70 (1998) 1003. [20] J. Klein, F. Beil, T. Halfmann, Phys. Rev. Lett. 99 (2007) 113003. [21] B.S. Ham, M.S. Shahriar, M.K. Kim, P.R. Hemmer, Opt. Lett. 22 (1997) 1849.