Slow and Stored Light in Atomic Vapor

My research program is focused on the manipulation of light pulse propagation through an atomic vapor and the development of efficient memory for a photon quantum state, and aimed to find the optimal operation conditions for practical realization of quantum information algorithms. The results of these experiments can be used later for better understanding of more complex systems (e.g. quantum dots or doped crystals).

The ability to control a quantum state of a photon is the first step in development of a new type of telecommunication which is based on quantum mechanical principles. In traditional optical communications information is carried by pulses of light in a 1-bit format (where detection of a pulse or no pulse stands for 1 and 0). However, quantum mechanics allows a photon to be in many states at the same time, so a quantum bit (q-bit) can carry much more information. Simultaneously, using quantum states of photons to carry information will increase the security of telecommunications. Quantum mechanics forbids duplicating a quantum state of a particle without destroying the original, which protects quantum network from eavesdropping, and makes them absolutely secure.

An important challenge in building a quantum network is the transmission of individual photons over long distances with high fidelity, since inevitable losses in optical fibers (which grow exponentially with distance) corrupt quantum information carried out by photons. To reliably transfer photons between two distant sites while preserving their individual quantum states, one needs to distribute "quantum repeaters" -- optical components which "purify" photon quantum states -- along a transmission channel and thus preserve the quantum information. Realization of quantum repeaters requires the development of quantum memory that is capable of storing, releasing and manipulating quantum states of individual photons.

One of the promising approaches is to use long-lived atomic states as quantum memory elements by mapping a quantum state of photons to a long-lived atomic state. This can be done by using an extra strong classical laser field which controls the propagation of weak probe photons through a resonant atomic medium, and creates a strong coupling between probe photons and the collective quantum state of atoms. Such coupling greatly reduces the light pulse velocity compare to light speed in vacuum ("slow light") while keeping the optical losses very low. Furthermore, by reducing the pulse velocity to zero the photonic state can be coherently transferred into the atomic quantum state. This process is completely reversible, i.e., the original photons can be recreated by turning the control field back on ("stored light"). Samples of slow and stored light pulse propagation are shown in Fig. 1.

The light storage technique, described above, is capable of transferring quantum states of light to atomic ensembles and back perfectly only under the condition of no dissipative optical losses and no decay of atomic quantum states. In realistic systems various loss mechanisms reduce the fidelity of the storage. Several research groups have already reported proof-of-principle experiments demonstrating essential tools for quantum networks, such as on-demand single photon generation and storage of a single photon in atomic ensemble. However, the efficiency and fidelity of these operations are still very low and must be improved dramatically before they can be used for practical applications.

We consider the propagation of a weak signal pulse with envelope E(t) and a strong, classical control field with Rabi frequency envelope Ω(t) in a resonant Λ-type atomic medium under conditions of EIT, as depicted in Fig. 3a. Each Λ-type atom possesses two long-lived electronic ground states, |g and |s, and a single excited state, |e, as in sub-levels of different angular momentum within the electronic ground state of alkali atoms. For our experiments, light fields were tuned near the 87Rb D1 (λ=795 nm) transition. States |g and |s corresponded to |F, mF=|1, 1, |2, 1, respectively; |e corresponded to |F, mF=|2, 2.

The control field creates a strong coupling between the signal field and a collective atomic spin excitation (spin wave). The two fields collaborate to place an atom into a coherent superposition of the two ground states, which no longer interacts with the optical fields. For a narrow range of signal field frequencies near the two-photon resonance, the previously-opaque medium is rendered transparent. The width of this so-called EIT window is determined by the strength of the control field,

,

where γ is the optical polarization decay rate and α is the absorption coefficient, so that αL is the optical depth of an atomic medium of length L. Accompanying this anomaly in the signal fields transmission spectrum is a very steep, linear change in the refractive index, resulting in a dramatically reduced group velocity for the signal pulse,

.

Since vg depends on the control fields intensity, pulse propagation through an EIT medium can be used as the basis for quantum memory. Figure 3(b) illustrates the three stages of the light storage process (writing, storage, and retrieval), while Figs. 3(c) and 3(d) show control and signal fields, respectively, during a typical experimental run. At the writing stage, a signal pulse Ein(t) is mapped onto spin wave S(z) by adiabatically reducing the control field (and hence vg) to zero. This spin wave is then preserved for some storage time τ, during which all optical fields are turned off. Lastly, the signal field Eout(t) is retrieved by re-illuminating the control field.

We characterize the memory by computing the storage efficiency as the probability of retrieving an incoming photon after storage, or equivalently, as the energy ratio between initial and retrieved signal pulses. To realize ideal storage (and optimize efficiency), two conditions must be met. On one hand, vg must be low enough to spatially compress the whole pulse of duration T into the length of the ensemble and avoid "leaking" the front edge of the pulse past the atoms (). On the other hand, all spectral components of the incoming pulse must fit inside the EIT transparency window to minimize spontaneous emission losses (). Simultaneously satisfying both conditions is possible only at high optical depth, .

We have demonstrated the efficacy of two memory optimization protocols. The first is based on the time-reversal symmetry of the storage process, which we exploit to iteratively determine an optimally-stored signal pulse for a given control field Ω(t). The first iteration step involves storing an arbitrary signal pulse. The efficiency of the retrieved signal is typically low. We electronically time-reverse and renormalize the retrieved pulse for use as the input pulse for the second iteration step. The storage efficiency grows with each iteration step until convergence. In Fig. 4(a), we depict the optimal signal pulses for three different control powers at an optical depth αL=24. In Fig. 4(b), we show the growth and convergence of memory efficiency at each step.  The second memory optimization protocol involves computing the control field shape needed to store a desired signal pulse. We have verified that this protocol is equally adept at producing the optimal memory efficiency.

In order to improve the memory efficiency, it is necessary to operate at high optical depth (high Rb concentration). We performed iterative optimization over a range of optical depths, as shown in Fig. 5. We clearly see that for optical depths up to αL=25, efficiency grows as theoretically predicted. Between αL=25 and 60, efficiency levels off; we suspected this was due to resonant FWM, discussed next. Above αL=60, storage efficiency degrades because unprepared atoms absorb the control field.

For low optical depths, it is sufficient to take into account only the effects of the single-Λ. However, due to resonant FWM, the far off-resonant interaction of the control field can spontaneously produce a Stokes optical field E', as shown in Fig. 6(a). Our experiments have indicated that the Stokes field can be slowed down during propagation [dashed red lines in Fig. 6(b)], and also detected upon retrieval from a storage experiment [solid red lines in Fig. 6(b)].

In order to understand the effects of FWM on light storage, we performed experiments in the cw, slow-, and stored-light regimes wherein we seeded the FWM process by sending an input Stokes field (in addition to input signal and control fields) into the vapor cell. We were able to adjust the relative amplitudes of the input signal and Stokes fields.

We developed a theoretical model of the EIT-FWM interaction, which accurately describes experimental observations and provides an intuitive understanding of light storage under FWM conditions. Figure 7 shows the results of storage experiments under EIT-FWM conditions and demonstrates the effectiveness of our model.