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This article is meant to be an addition to the Slow light article already on Wikipedia.

Stopped Light

Stopped Light is a phenomenon where information can be coherently transfered from light to matter and back. It has been accomplished in a number of ways including using techniques like electromagnetically induced transparency (EIT), controlled reversible inhomogeneous broadening (CRIB), and atomic frequency combs (AFC), among others. Stopping light is important for applications in quantum memory, as it provides a means to take information from a coherent light pulse and store it before extracting it in its exact coherent state after a given amount of time. It also provides a means to study the dynamics of Bose-Einstein condensates (BECs).

Theory

Electromagnetically Induced Transparency

Figure 1: Λ-configuration system 3-level EIT system used in stopping light. Atoms are initially in state |g⟩. A coupling laser tuned to the |m⟩→|e⟩ transition illuminates the system with a probe pulse resonant with the |g⟩→|e⟩ transition. While both are on, the system is transparent to the probe pulse. When the coupling laser is turned off, the probe pulse is stopped inside the system, and remains there until the coupling laser is turned back on.

One notable technique used for stopping light is by using EIT in three level Λ-configuration systems (see Figure 1). The system of atoms must first be brought into a single internal quantum state, |1⟩, which is then illuminated by coupling and probe laser fields. The coupling laser, resonant with the |2⟩↔|3⟩ transition, is much stronger than the probe laser pulse which is resonant with the |1⟩↔|3⟩ transition. This has the effect of putting the atoms in the region of the probe pulse into the dark state

$$|D\rangle ={\frac {\Omega _{c}|1\rangle -\Omega _{p}|2\rangle \exp[i({\textbf {k}}_{p}-{\textbf {k}}_{c})\centerdot {\textbf {r}}-i(\omega _{p}-\omega _{c})t]}{\sqrt {\Omega _{c}^{2}+\Omega _{p}^{2}}}}$$

Figure 2: EIT Dispersion Absorption lines of the atomic medium are shown in gray and its index of refraction is shown in blue as a function of frequency. In the narrow band of frequencies where the absorption is zero, the index of refraction has a very steep slope which slows the light by orders of magnitude.

which is a coherent superposition of the |1⟩ and |2⟩ states. Here $\Omega _{p,c}$ are the Rabi frequencies, ${\textbf {k}}_{p,c}$ are the wave vectors, and $\omega _{p,c}$ are the optical angular frequencies of the probe and coupling lasers respectively, with $\Omega _{c}>>\Omega _{p}$. This state prevents absorption over a very narrow band of frequencies, effectively making the medium of atoms transparent to the probe laser. This also causes a very steep change in refractive index, which slows the group velocity of the light passing through by at least 7 orders of magnitude (see Figure 2). Because of this slowing, the pulse, depending on its initial length/duration, is compressed such that it is able to fit entirely within the atomic medium.

As the probe pulse passes through the system, its coherence is mapped onto the atoms' wavefunction, imprinting information about its amplitude and phase. As long as the coupling laser is on, the EIT allows the probe pulse to slowly pass through. However, when the coupling laser is turned off, the pulse becomes trapped in the now opaque medium, locking the atoms in the dark state and storing the coherent information from the probe pulse. At some later time, once the coupling laser is turned back on, stimulated emission regenerates the probe pulse and it continues to pass through the atoms via EIT as though nothing had changed.

Early Experiments

Using Atomic Vapors

In 2000 a group from the Harvard-Smithsonian Center for Astrophysics stopped and stored light in a cloud of atomic rubidium atoms at ~70-90° C. These experiments used the $5^{2}S_{1/2},F=2\rightarrow 5^{2}P_{1/2},F=1$ transition of ${\ce {^{87}Rb}}$ with Zeeman splitting of the first level. Initially, most of the atoms were kept in the ${\textstyle 5^{2}S_{1/2},F=2,M_{F}=+2}$ magnetic sublevel and a coupling field was applied that was in resonance with the transition between this level and the $5^{2}P_{1/2},F=1$ level. The probe pulse was tuned to the ${\textstyle 5^{2}S_{1/2},F=2,M_{F}=0\rightarrow 5^{2}P_{1/2},F=1}$ transition. Using this setup and configuration, they were able to store light for up to about 0.5 ms.

These light storage times are limited by decoherence, caused by Rb atoms escaping the interaction region and spin-exchange collisions causing spin coherence decays.

Using Ultracold Atomic Gasses

In 2001, another group of scientists from Harvard University and the Rowland Institute for Science managed to store light in a system of cold atoms. In order to have a system of atoms all initially in a single common state, the team cooled and magnetically trapped a cloud of sodium atoms to 0.9 μK, just above the critical temperature for Bose-Einstein condensation. They illuminated these atoms with a coupling laser tuned to the $|3S,F=2,M_{F}=+1\rangle \rightarrow |3P,F=2,M_{F}=0\rangle$ transition and a probe pulse resonant with the $|3S,F=1,M_{F}=-1\rangle \rightarrow |3P,F=2,M_{F}=0\rangle$ transition. Using this setup, they were able to successfully store light for over 0.8 ms.

Because these systems were not cooled all the way down to BECs, atomic wavefunctions were able to evolve due to external dynamics such as thermal diffusion, kinetic energy, external trapping potentials and atom-atom interactions, which led to decohering of the stored information inside of the atom cloud, thus limiting the amount of storage time.

Further Developments

As time has gone on, researchers have worked to extend the storage time of light in matter. The group of scientists from the 2001 experiment mentioned above extended the storage times by further cooling their atoms to Bose Einstein Condensates. In so doing, they were able to avoid all of the decoherence caused by thermal diffusion, which allowed them to increase their storage times to the order of seconds.

Scientists have also explored using EIT in rare-earth-ion-doped-crystals (REIC). Because REICs have longer coherence times and do not suffer from atomic diffusion, they have the capability of achieving longer memories. In 2005, scientists were able to stop light in REICs on the order of seconds. By applying external magnetic fields to the REIC, it is possible to further increase the coherence times, thus extending the time which light can be stored inside. However, introducing these fields also introduces hyperfine transitions into the system which leads to complex energy structures. Using several different techniques to optimize which energy levels had the longest coherence times, a group managed to stop and store light in ${\ce {Y_2SiO_5}}$ on the order of 1 minute in 2013.