We demonstrate a cooperative optical non-linearity caused by dipolar interactions between Rydberg atoms in an ultra-cold atomic ensemble. By coupling a probe transition to the Rydberg state we map the strong dipoledipole interactions between Rydberg pairs onto the optical field. We characterize the non-linearity as a function of electric field and density, and demonstrate the enhancement of the optical non-linearity due to cooperativity. PACS numbers: 42.50.Nn, 32.80.Rm, 34.20.Cf, 42.50.Gy Photons are robust carriers of quantum information and consequently there is considerable interest in the development of photonic quantum technologies. As optical non-linearities are extremely small at the single photon level [1] attention has focussed on linear optical quantum computing [2,3]. In parallel, work has been carried out on materials with a large Kerr effect [4,5,6,7,8] potentially enabling non-linear photonic devices. Theoretical work has explored some of the difficulties in realizing a high fidelity quantum gate based on the Kerr effect [9]. An alternative mechanism for generating an optical non-linearity, for example a cooperative non-linearity due to dipolar interactions, could open new avenues for photonic quantum gates [10]. In a dipolar system the electric field is modified due to the local field of the neighbouring dipoles [11]. Such local field effects can give rise to cooperative behaviour such as superradiance [12,13] and optical bistability [14,15].In this paper we demonstrate a cooperative optical nonlinearity due to dipole-dipole interactions between Rydberg atoms. These strong interatomic interactions are sufficient to prevent excitation of neighbouring atoms to the Rydberg state [16] . This gives rise to a blockade mechanism which has been observed for a pair of trapped atoms [17,18] and an atomic ensemble [19]. In our work the effect of strong interactions between Rydberg pairs is mapped onto an optical transition using electromagnetically induced transparency (EIT) [20,21]. The resonant dark state responsible for EIT is modified by the dipole-dipole interactions, causing suppression of the transparency on resonance. The resulting optical non-linearity depends on interactions between pairs of atoms and is a cooperative effect where the optical response of a single atom is modified by the presence of its neighbours.To show how dipole-dipole interactions give rise to a cooperative non-linear effect, we consider the atom pair model [22] shown in fig. 1(a) for three level atoms with ground |g , excited |e , and Rydberg |r states. These states are coupled by a probe laser with Rabi frequency Ω p and a strong coupling laser with Rabi frequency Ω c . In the non-interacting case with probe and coupling lasers tuned to resonance the dark state is [23]: where tan θ = Ω p /Ω c and φ r is the relative phase between probe and coupling lasers. This state is not coupled to the probe field, leading to 100 % transparency independent of the mixing angle, θ. Dipole-dipole interactions modify this picture. The effe...

We use a microwave field to control the quantum state of optical photons stored in a cold atomic cloud. The photons are stored in highly excited collective states (Rydberg polaritons) enabling both fast qubit rotations and control of photon-photon interactions. Through the collective read-out of these pseudospin rotations it is shown that the microwave field modifies the long-range interactions between polaritons. This technique provides a powerful interface between the microwave and optical domains, with applications in quantum simulations of spin liquids, quantum metrology and quantum networks.

We demonstrate a non-equilibrium phase transition in a dilute thermal atomic gas. The phase transition, between states of low and high Rydberg occupancy, is induced by resonant dipole-dipole interactions between Rydberg atoms. The gas can be considered as dilute as the atoms are separated by distances much greater than the wavelength of the optical transitions used to excite them. In the frequency domain we observe a mean-field shift of the Rydberg state which results in intrinsic optical bistability above a critical Rydberg number density. In the time domain we observe critical slowing down where the recovery time to system perturbations diverges with critical exponent α = −0.53 ± 0.10. The atomic emission spectrum of the phase with high Rydberg occupancy provides evidence for a superradiant cascade.Non-equilibrium systems displaying phase transitions are found throughout nature and society, for example in ecosystems, financial markets and climate [1]. The steady state of a non-equilibrium system is a dynamical equilibrium between driving and dissipative processes. In atomic physics, one of the most studied non-equilibrium phase transitions is optical bistability where the driving is provided by a resonant laser field and the dissipation is inherent in the atom-light interaction. In most examples of optical bistability feedback is provided by an optical cavity, as in the pioneering work of Gibbs [2,3]. However, bistability can also arise in systems where many dipoles are located within a volume which is much smaller than the optical wavelength; in this case the feedback is due to resonant dipole-dipole interactions [4,5]. This latter case is known as intrinsic optical bistability [6] and has, so far, only been observed in an up-conversion process between densely packed Yb 3+ ions in a solid-state crystal host cooled to cryogenic temperatures [7]. Intrinsic optical bistability generally cannot be observed for simple two-level systems such as atomic gases, because the resonance broadening, which is larger than the line shift [8], suppresses the bistable response [9,10].A solution to this problem is provided by highlyexcited Rydberg states, where the dipole-dipole induced level shifts between neighbouring states can be much larger than the excitation linewidth. This property of optical excitation of Rydberg atoms, known as dipole blockade [11], enables a diverse range of applications in quantum many-body physics, quantum information processing [12], non-linear optics [13] and quantum optics [14][15][16][17]. An interesting feature of Rydberg systems is that the range of the interaction can be much larger than the optical excitation wavelength, giving rise to non-local interactions [18]. This also creates the possibility of observing intrinsic optical bistability, and hence non-equilibrium phase transitions [19] over macroscopic, optically-resolvable length scales.In this letter, we demonstrate a non-equilibrium phase transition in a thermal Rydberg ensemble. In contrast to previous experiments, we directly observe...

No abstract

The electro-optic effect, where the refractive index of a medium is modified by an electric field, is of central importance in non-linear optics, laser technology, quantum optics and optical communications. In general, electro-optic coefficients are very weak and a medium with a giant electro-optic coefficient would have profound implications for non-linear optics, especially at the single photon level, enabling single photon entanglement and switching. Here we propose and demonstrate a giant electro-optic effect based on polarizable dark states. We demonstrate phase modulation of the light field in the dark state medium and measure an electro-optic coefficient that is more than 12 orders of magnitude larger than in other gases. This enormous Kerr non-linearity also creates the potential for precision electrometry and photon entanglement.PACS numbers: 32.80.Rm, 42.50.Gy In 1875 Kerr showed that the refractive index (n r ) of a medium can be changed by applying an electric field [1] according to ∆n r = λ 0 B 0 E 2 0 , where λ 0 is the wavelength of the light field, E 0 is the applied electric field and B 0 is the electro-optic Kerr coefficient. Subsequently, the Kerr effect, or quadratic electro-optic effect, and the related linear electro-optic effect have become widely used in photonic devices such as electro-optic modulators (EOMs) [2,3]. The ac Kerr effect where the electric field is produced by another light beam is the basis of Kerr lens mode-locking [4], and has led to the development of femto and attosecond pulses [5]. Outside these successes, the wider applicability of the Kerr effect is limited by the fact that, in general, the Kerr non-linearity is very small. A larger non-linearity occurs close to a resonance, but at the expense of higher absorption of the signal light. A way around this problem is to use electromagnetically induced transparency (EIT) [6,7,8] where an additional light field, the coupling beam, renders a medium transparent on resonance. Enhanced ac Kerr non-linearities were predicted [9], and have been studied in experiments on Bose Einstein condensates [10] and cold atoms [11]. However, such an EIT medium produces insufficient non-linearity to implement single photon non-linear optics [8]. In addition, the potential to implement all-optical quantum computation using the ac Kerr effect [12] is limited by pulse distortion effects [13], so a new Kerr mechanism based on interactions [14] is desirable.In this paper, we demonstrate a giant dc electro-optic effect in an EIT medium by coupling to a highly excited Rydberg state which has a large polarizability. This renders the transmission through the medium highly sensitive to electric fields produced either externally or internally due to interparticle interactions. The Rydberg states have a polarizability that scales as the principal quantum number, n 7 , and the interactions between Rydberg atoms scale with an even higher power (n 11 for van der Waals interactions) [15]. These strong interac-tions lead to strongly correlated quantum st...

Terahertz (THz) near-field imaging is a flourishing discipline [1, 2], with applications from fundamental studies of beam propagation [3] to the characterisation of metamaterials [4,5] and waveguides [6,7]. Beating the diffraction limit typically involves rastering structures or detectors with length scale shorter than the radiation wavelength; in the THz domain this has been achieved using a number of techniques including scattering tips [8,9] and apertures [10]. Alternatively, mapping THz fields onto an optical wavelength and imaging the visible light removes the requirement for scanning a local probe, speeding up image collection times [11,12]. Here we report THz to optical conversion using a gas of highly excited 'Rydberg' atoms. By collecting THz-induced optical fluorescence we demonstrate a real-time image of a THz standing wave and we use well-known atomic properties to calibrate the THz field strength.Atoms make excellent electromagnetic field sensors because narrow line-width atomic transitions couple strongly to EM fields, giving atoms a sensitive, narrowband response. In addition, each atom of the same isotope is identical and has well studied, permanent properties which facilitate easy calibration to SI units. Atomic states that couple to multiple transitions offer an interface between different frequency regimes. In this way atomic ground states have been used to map microwave fields onto an optical probe [13]. However atomic ground states are only sensitive to a limited selection of microwave frequencies. In contrast, highlyexcited Rydberg atoms couple to strong, electric dipole transitions across a wide range of microwave and THz frequencies, making them ideal candidates for field measurement and for frequency standards in the millimeter wave and THz range [14]. Previous methods for THz imaging with Rydberg atoms used the THz radiation to ionise the atoms [15,16]. More recently optical read-out of Rydberg states was demonstrated in a room-temperature alkali-metal vapour using electromagnetically induced transparency (EIT) [17]. The 'Rydberg EIT' technique has since been exploited to readout radio frequency fields [18], to demonstrate precision microwave electrometry [19][20][21] and for sub-wavelength imaging of microwave fields [22]. * c.g.wade@durham.ac.ukIn distinction to the EIT technique we make direct use of THz-induced optical fluorescence to demonstrate THz imaging. An overview of our THz imaging setup is shown in Figure 1a. Infrared laser beams forming a three-step ladder excitation scheme [23] are co-axially aligned with a continuous wave (CW) THz beam and pass through a caesium vapour in a 2 mm long quartz cell. In regions where both the THz field and the laser beams are present, atoms are excited to a Rydberg state and subsequently decay with fluorescence at visible wavelengths. The fluorescence is imaged by a consumer digital camera, and a typical 0.5 s exposure is shown in Figure 1b. In Figure 1c we show THz transition frequencies and calculated reduced dipole matrix elements,d, for...

The implementation of electromagnetically induced transparency (EIT) in a cold Rydberg gas provides an attractive route towards strong photon-photon interactions and fully deterministic all-optical quantum information processing. In this brief review we discuss the underlying principles of how large single photon non-linearities are achieved in this system and describe experimental progress to date. CONTENTS

We demonstrate laser frequency stabilization to excited state transitions using cascade electromagnetically induced transparency. Using a room temperature Rb vapor cell as a reference, we stabilize a first diode laser to the D2 transition and a second laser to a transition from the intermediate 5P 3/2 state to a highly excited state with principal quantum number n = 19 − 70. A combined laser linewidth of 280 ± 50 kHz over a 100 µs time period is achieved. This method may be applied generally to any cascade system and allows laser stabilization to an atomic reference in the absence of a direct absorption signal.