## Abstract

Coherent wave splitting is crucial in interferometers. Normally, the waves after this splitting are of the same type. But recent progress in interactions between atom and light has led to the coherent conversion of photon to atomic excitation. This makes it possible to split an incoming light wave into a coherent superposition state of atom and light and paves the way for an interferometer made of different types of waves. Here we report on a Rabi-like coherent-superposition oscillation observed between an atom and light in a Raman process. We construct a new kind of hybrid interferometer based on the atom–light coherent superposition state. Interference fringes are observed in both the optical output intensity and atomic output in terms of the atomic spin wave strength when we scan either or both of the optical and atomic phases. Such a hybrid interferometer can be used to interrogate atomic states by optical detection and will find its applications in precision measurement and quantum control of atoms and light.

© 2016 Optical Society of America

## 1. INTRODUCTION

In quantum storage, complete conversion of quantum states between atoms and light is essential for the high-fidelity transfer of quantum information. Quantum storage was first realized with the method of electromagnetically induced transparency [1–6] and then by gradient echo memory [7–9]. More recently, Raman processes were used to achieve wide-band quantum storage [10–12]. On the one hand, most research concentrated on increasing the efficiency of quantum storage because a partial conversion is usually regarded as a loss for the quantum system and leads to a reduction in the fidelity of quantum information transfer. But the unconverted part still contains the original information. So, if available, it can be further converted [13] for better overall conversion efficiency. On the other hand, since quantum storage is coherent in the sense that the phase of the quantum states is preserved, the converted and the unconverted parts are coherent to each other. This property can be employed for quantum interference. In 2012, Campbell *et al.* [14] achieved coherent mixture of an atomic wave and an optical wave in an atom-photon polariton state with a gradient echo memory scheme. Later, Pinel *et al.* [15] demonstrated a mirrorless spin wave resonator based on multiple interferences between light and an atomic spin wave. Such an interference effect was also the mechanism for a mirrorless oscillation in an atomic Raman process [16].

Rabi oscillation is a coherent population oscillation between two atomic levels when driven by a strong coherent radiation field coupled to the two levels [17]. It plays an important role in atomic clocks by forming a Ramsey atomic interferometer [18]. Two-photon Rabi oscillation was also realized in an atomic Raman system where two strong driving fields are present [19]. Recently, Rabi oscillation between photons of a Raman write field and the frequency-offset Stokes field was demonstrated [20] in a Raman process where the driving field was a strong atomic spin wave. Here, the roles were reversed for atom and light as compared to the traditional Rabi oscillation effect. It was recently predicted [21] that Rabi-like coherent-superposition oscillation between light and an atom can also occur in an atomic Raman process. When the driving field is a $\pi $-pulse, it is possible to make a complete conversion from light to atom for quantum storage or from atom to light for readout.

However, when the driving field is a $\pi /2$-pulse, we can achieve a coherent wave splitting of the input field into an optical wave and an atomic wave. The reverse process is just a coherent mixing of an optical wave and an atomic spin wave. Thus, it is possible to form a new type of interferometer made of an atom and light. In contrast to the traditional interferometers, which are constructed with linear beam splitters for coherent splitting into and mixing of the same type of wave and are only sensitive to the phase shift of one type of wave, this new hybrid atom–light interferometer involves waves of different types and should depend on the phases of both optical and atomic waves. This is somewhat similar to an SU(1,1) type atom–light interferometer recently realized by our group [22], whose beam splitting process is an SU(1,1)-type parametric Raman amplifier instead of an SU(2) linear beam splitter in the current scheme [23,24].

In this paper, we report on the first observation of Rabi-like superposition oscillation between light and an atom in a Raman process involving Rb-atoms and a demonstration of an atom–light interferometer by employing this Rabi-like superposition oscillation effect as an atom and light wave splitter and mixer. This is a Ramsey-type interferometer in the sense that a strong driving laser in $\pi /2$-pulse area creates a superposition between the atom and light, and after a time delay with the evolution of both the atom and light, another $\pi /2$-pulse laser is applied to mix the atom and light for interference. In additional to the usual dependence on the optical phase, we find that the interference fringes also depend on the atomic phase, which is sensitive to a variety of physical quantities. Thus, this type of interferometer can be applied in precision measurement, the sensitive measurement of atomic states, and the quantum control of light and atoms.

## 2. ATOM–LIGHT SUPERPOSITION OSCILLATION

The process we use to mix atomic and optical waves is the collective Raman process in an ensemble of ${N}_{a}$ three-level atoms. The process is depicted in Fig. 1(a), with the atomic levels and optical frequencies shown in Fig. 1(b). In the process, a pair of lower-level meta-stable states $|g\u27e9,|m\u27e9$ is coupled to the Raman write field ($W$, or ${\widehat{a}}_{W}$) and the Stokes field ($S$, or ${\widehat{a}}_{S}$) via an upper excited level ${e}_{1}$. After adiabatically eliminating the upper excited level ${e}_{1}$, this process is a three-wave mixing process involving the write field, the Stokes field, and a collective atomic pseudo-spin field ${\widehat{S}}_{a}\equiv (1/\sqrt{{N}_{a}})\sum _{k}{|g\u27e9}_{k}\u27e8m|$, and the coupling Hamiltonian is given by [25,26]

It is interesting to see that if there is only one input field, say, the write field (${I}_{W}^{(0)}\ne 0$), the intensities of the output fields are ${I}_{W}={I}_{W}^{(0)}\text{\hspace{0.17em}}{\mathrm{cos}}^{2}(\theta /2)$, ${I}_{{S}_{a}}={I}_{W}^{(0)}\text{\hspace{0.17em}}{\mathrm{sin}}^{2}(\theta /2)$, which oscillate in time with a frequency proportional to ${A}_{S}$, the amplitude of the strong Stokes field. This resembles the Rabi oscillation in a two-level system driven by a strong field [17]. Here, the oscillation is between the write field and the atomic spin wave instead of the atomic levels, while the strong Stokes field (${A}_{S}$) is the driving field. Similar oscillation occurs if only the atomic spin wave is initially non-zero (${I}_{{S}_{a}}^{(0)}\ne 0$): ${I}_{W}={I}_{{S}_{a}}^{(0)}\text{\hspace{0.17em}}{\mathrm{sin}}^{2}(\theta /2)$, ${I}_{{S}_{a}}={I}_{{S}_{a}}^{(0)}\text{\hspace{0.17em}}{\mathrm{cos}}^{2}(\theta /2)$. On the other hand, if both fields are initially non-zero, the outputs are coherent mixtures of the two fields with mixing coefficients $\mathrm{sin}(\theta /2)$ and $\mathrm{cos}(\theta /2)$.

For the experimental observation of the Rabi-like superposition oscillation between light and the atom, we can approach it by either preparing the atoms with an initial atomic spin wave or simply injecting a write field. The experimental sketch is shown in Fig. 1(c) with the timing sequence in Fig. 1(d1). In the first approach, atoms are initially prepared with a non-zero spin wave by two pulses of ${\mathrm{S}}_{0}$ and ${\mathrm{W}}_{0}$ (see Appendix A for detail). After a short delay, a strong Stokes driving pulse (${A}_{S}$) of 0.2 μs length is sent in the opposite direction into the cell to drive the Rabi-like superposition oscillation. To observe it, the $W$-field (${\widehat{a}}_{W}^{\text{out}}$) is measured by a photodetector and recorded in an oscilloscope. Figure 2(a) shows a typical run, clearly demonstrating the oscillation effect. The amplitude decay is due to the decoherence of the atomic spin wave. Figure 2(b) shows the oscillation frequency as a function of the amplitude ${A}_{S}$ of the strong driving Stokes field. The linear dependence confirms it as a Rabi frequency, as given in Eq. (3). For the case of initial injection at the $W$-field (${\widehat{a}}_{W}^{\text{in}}$ shown in Fig. 1), we need to lock its frequency to the strong Stokes driving field to within several hundred Hertz to satisfy the requirement of the two-photon resonance condition: ${\omega}_{W}-{\omega}_{S}={\omega}_{gm}$. The time sequence is shown in Fig. 1(d2). Figure 2(c) shows a typical run for this case. The oscillation frequency is confirmed in Fig. 2(d) as the Rabi frequency given in Eq. (3). Notice that the curves in Figs. 2(a) and 2(c) are complementary to each other, reflecting the sine and cosine functions in Eq. (3).

## 3. ATOM–LIGHT HYBRID INTERFEROMETER

From Eq. (3), we find when we adjust the pulse width or amplitude of the Stokes field so that $\theta =\pi $, the oscillation stops at the maximum conversion between the atom and light. Notice that the Hamiltonian in Eq. (2) is in the form of an SU(2) interaction between atoms and light [24], and the input–output relation in Eq. (3) is exactly the relation for a lossless beam splitter [24,27]: the write field here is equivalent to one of the input fields of the beam splitter, and the atomic spin wave is the other field. Thus, the outputs are coherent mixtures of the optical field and the atomic spin wave. When the pulse width satisfies $\theta =\pi /2$, only half will be converted, and this leads to a coherent atom–light wave splitting.

Next, we use this atom–light wave splitter to form an atom–light interferometer. As shown in Fig. 3, after the first splitting of the incoming wave (the initially prepared atomic spin wave here in our experiment), we mix the split atom and light waves with another similar conversion process. This is done by redirecting the generated $W$-field (${\mathrm{W}}_{1}$) back to the atomic cell that contains the unconverted atomic spin wave and mixing them with another Stokes $\pi /2$-pulse. To separate the splitting and the mixing processes, a delay between the two Stokes $\pi /2$ pulses is introduced with a 100 m-long single-mode fiber (${\mathrm{SMF}}_{0}$). A similar delay with another ${\mathrm{SMF}}_{1}$ is introduced in the returned $W$-field.

To make a comparison with a conventional interferometer with beam splitters, the first pulse will act as the Raman read field in the first Raman read process to split the initially prepared atomic spin wave ${S}_{a0}$ into half write field (${\mathrm{W}}_{1}$) and half-spin wave (${S}_{a1}$). This process can be regarded as the first beam splitter in the conventional interferometer. The lengths of the two SMFs are made equal to ensure that the delayed Stokes pulse (${\mathrm{S}}_{2}$) and the write field ${\mathrm{W}}_{1}$ generated in the first Raman process and fed back to the cell will enter the vapor cell that contains the spin wave ${S}_{a1}$ at the same time to carry out the second Raman process for mixing ${S}_{a1}$ and ${\mathrm{W}}_{1}$, i.e., the second beam splitter process. In between the first splitting and the second mixing processes, we introduce a phase modulation unit (piezoelectric transducer, PZT) in ${\mathrm{W}}_{1}$’s path to change its phase. The final light signal in the write field (${\mathrm{W}}_{2}$) after the second beam splitter is collected with another single-mode fiber (${\mathrm{SMF}}_{2}$) and detected after an etalon, which is used to filter out the leaked strong Stokes photons. The atomic signal after the second beam splitter can be converted into the light field (${\mathrm{W}}_{3}$) by injecting another strong read pulse (${\mathrm{S}}_{3}$) right after the second Stokes pulse (${\mathrm{S}}_{2}$). The conversion efficiency is about 20%. This signal is also collected by ${\mathrm{SMF}}_{2}$ and detected after the etalon. So we will observe two temporally separated pulses by the detector: the first one from ${\mathrm{W}}_{2}$, and the second one from ${\mathrm{W}}_{3}$. The heights of the two pulses correspond to the intensities of the final write field (${\mathrm{W}}_{2}$) and the final atomic spin wave ${S}_{a2}$, respectively. Figure 4 shows the interference fringes detected in both the output $W$-field and the final atomic spin wave. The solid lines are the best fits to the cosine function with visibilities of 96.6% and 94.8%, respectively.

Since the atomic spin wave is involved in this interference scheme, the interference fringes should depend on the phase of the atomic spin wave as well, which can be changed by some external fields, such as the magnetic field and electric field. However, dependence on the magnetic field relies on the magnetic sub-levels and can be very complicated. Here, we resort to an AC Stark effect [28] for the atomic phase change. It is well known that when atoms are subject to the illumination of an electromagnetic field, their energy level will be shifted. For the atomic Raman process discussed previously, the AC Stark shift is given by the amount of [26,29]

## 4. DISCUSSION

In summary, we demonstrate coherent conversion between an atom and light in the form of a Rabi-like oscillation. This coherent conversion process can be used as a wave splitter into the coherent superposition of an atomic spin wave and an optical wave and as a wave mixer of the coherent atomic spin wave and optical wave. We construct an atom–light hybrid interferometer in which the interference fringes depend on both the optical phase and atomic phase. The intensity-dependent atomic phase shift can be used for a quantum non-demolition measurement (QND) [30–32] of the photon number of the phase-inducing field (the 780 nm laser beam in our experiment). This is similar to the QND measurement in the optical Kerr effect [33–35]. Furthermore, the atomic phase can be changed by other means such as magnetic and electric fields. So, this atom–light interferometer will have wide applications in precision measurement, quantum metrology, and quantum control of atom and light.

It should be pointed out that the mechanisms of the current atom–light interferometer and atom interferometers [18,36–38] are different, though the processes to split and recombine the interference beams are both Raman processes with the interaction Hamiltonian given in Eq. (1) [39] and the interference fringes depend on both the optical and atomic phases. For the atom interferometers, the optical fields are the driving fields for the superposition of the same type of waves of atomic states (either internal states in the Ramsey interferometer or external states in the matter-wave interferometer), and the driving fields do not participate in the actual interference, but only appear as parameters in the coefficients of the superposition states. For our current Ramsey-like atom–light interferometer, the Stokes driving field creates a superposition between different waves of light (write field) and the atom (spin wave) and so the two interfering fields are different types. It is interesting to note that even though the two interfering fields are different, in an apparent violation of Dirac’s famous statement on photon interference, i.e., a photon only interferes with itself [40], the final fields observed by the detectors are still the same type and it is still indistinguishability that leads to the interference effect.

## APPENDIX A

In the experiment, the atomic medium is Rubidium-87 atoms which is contained in a 50 mm long paraffin coated glass cell. The energy levels of the Rb atom are shown in Fig. 1(b), where states $|g\u27e9$ and $|m\u27e9$ are the two ground states (${5}^{2}{S}_{1/2},F=1,2$) from hyperfine splitting and $|{e}_{1}\u27e9$, $|{e}_{2}\u27e9$ are two excited states (${5}^{2}{P}_{1/2},F=2,{5}^{2}{P}_{3/2}$). An optical pumping field (OP), tuned to $|m\u27e9\to |{e}_{2}\u27e9$ transition at 780 nm, is used to prepare the atoms in $|g\u27e9$ state. The power and waist of OP laser is 200 mW and 2.0 mm, respectively. To get the initial atomic spin wave ${S}_{a0}$, we apply the Raman write field (${W}_{0}$) and Stokes seed (${S}_{0}$) simultaneously to perform a stimulated Raman scattering. The write laser is blue-detuned about 1.5 GHz from $|g\u27e9\to |{e}_{1}\u27e9$ transition. The Stokes seed we used comes from the same laser as the ${W}_{0}$ beam but its frequency is red-shifted 6.8 GHz from ${W}_{0}$ beam in another vapor cell using feedback Raman scattering [41]. In Fig. 2, the power of ${W}_{0}$ and ${S}_{0}$ fields are 1.0 mW and 0.5 μW, respectively. The waists of ${W}_{0}$ and ${S}_{0}$ fields are both 0.4 mm. In Fig. 4, the power of ${W}_{0}$, ${S}_{0}$ and ${S}_{3}$ fields are 3.0 mW, 2.0 μW and 10 mW, respectively. The powers of ${S}_{1}$ and ${S}_{2}$ fields are 10 mW and 30 mW, respectively. The waists of ${S}_{0}$, ${W}_{0}$, ${S}_{1}$, ${S}_{2}$, ${S}_{3}$ and probe beams are all 1.0 mm. The vapor cell is placed inside a four-layer magnetic shielding to reduce stray magnetic fields and is heated up to 75° corresponding to atomic density of ${10}^{11}\u2013{10}^{12}/{\mathrm{cm}}^{3}$ using a bifilar resistive heater. The density of the atomic sample is an important parameter for Rabi-like oscillation and hybrid interferometer because $\mathrm{\Omega}=2\eta {A}_{S}^{*}\propto \sqrt{{N}_{a}}$. The oscillation between light and atoms can be observed only when oscillation period is shorter than the decoherence time. In our experimental system, the coherence time of atomic spin wave is about 0.2 μs for 0.4 mm beam waist and 0.5 μs for 1.0 mm beam waist, which is mainly limited by the atomic diffusion while the magnetic inhomogeneity effect can be ignored because of four-layer magnetic shielding.

## Funding

National Key Research Program of China (2016YFA0302000); National Natural Science Foundation of China (NSFC) (11129402, 11234003, 11274118, 91536114); Shanghai Municipal Education Commission (13ZZ036).

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