The spectral purity of an oscillator is central to many applications, such as detecting gravity waves, defining the second, ground-state cooling and quantum manipulation of nanomechanical objects, and quantum computation. Recent proposals suggest that laser oscillators which use very narrow optical transitions in atoms can be orders of magnitude more spectrally pure than present lasers. Lasers of this high spectral purity are predicted to operate deep in the 'bad-cavity', or superradiant, regime, where the bare atomic linewidth is much less than the cavity linewidth. Here we demonstrate a Raman superradiant laser source in which spontaneous synchronization of more than one million rubidium-87 atomic dipoles is continuously sustained by less than 0.2 photons on average inside the optical cavity. By operating at low intracavity photon number, we demonstrate isolation of the collective atomic dipole from the environment by a factor of more than ten thousand, as characterized by cavity frequency pulling measurements. The emitted light has a frequency linewidth, measured relative to the Raman dressing laser, that is less than that of single-particle decoherence linewidths and more than ten thousand times less than the quantum linewidth limit typically applied to 'good-cavity' optical lasers, for which the cavity linewidth is much less than the atomic linewidth. These results demonstrate several key predictions for future superradiant lasers, which could be used to improve the stability of passive atomic clocks and which may lead to new searches for physics beyond the standard model.

We propose a new light source based on having alkaline-earth atoms in an optical lattice collectively emit photons on an ultra-narrow clock transition into the mode of a high Q-resonator. The resultant optical radiation has an extremely narrow linewidth in the mHz range, even smaller than that of the clock transition itself due to collective effects. A power level of order 10 −12 W is possible, sufficient for phase-locking a slave optical local oscillator. Realizing this light source has the potential to improve the stability of the best clocks by two orders of magnitude.PACS numbers: 42.50. Nn, 06.30.6v, 37.10.Jk, 37.30.+i, 46.62.Eh Time and frequencies are the quantities that we can measure with the highest accuracy by far. From this fact derives the importance of clocks and frequency standards for many applications in technology and fundamental science. Some applications directly relying on atomic clocks are GPS, synchronization of data and communication networks, precise measurements of the gravitational potential of the earth, radio astronomy, tests of theories of gravity, and tests of the fundamental laws of physics.With the advent of octave spanning optical frequency combs [1,2] it has become feasible to use atomic transitions in the optical domain to build atomic clocks. Optical clocks based on ions [3] and ultracold neutral atoms confined in optical lattices [4] have recently demonstrated a precision of about 1 part in 10 15 at one second and a total fractional uncertainty of 10 −16 [4] or below [3], surpassing the primary cesium microwave standards [5,6].The state-of-the-art optical atomic clocks do not achieve the full stability that is in principle afforded by the atomic transitions on which they are founded. These transitions could have natural line-Qs of order 10 18 , exceeding the fractional stability of the clocks by a factor of ∼ 100. The main obstacle that prevents us from reaping the full benefit of the ultra-narrow clock transitions is the linewidth of the lasers used to interrogate these transitions. These lasers are stabilized against carefully designed passive high-Q cavities and achieve linewidths < 1 Hz, making them the most stable coherent sources of radiation. It is mainly the thermal noise of the reference cavity mirrors that prevent a further linewidth reduction [7] and substantially reducing this noise is hard [8].An elegant solution to these problems would be to directly extract light emitted from the ultra-narrow clock transition [9]. That light could then be used as an optical phase reference, circumventing the need for an ultra stable reference cavity. Unfortunately, the fluorescence light emitted on a clock transition is too weak for practical applications. For instance, for 10 6 fully inverted 87 Sr atoms the power of the spontaneously emitted light is of the order of 10 −16 W.The key observation that motivates this work is that if we could coerce the ensemble of atoms to emit the energy stored in them collectively rather than individually, the resulting power of order 10 −...

Alkaline-earth like atoms with ultra-narrow optical transitions enable superradiance in steady state. The emitted light promises to have an unprecedented stability with a linewidth as narrow as a few millihertz. In order to evaluate the potential usefulness of this light source as an ultrastable oscillator in clock and precision metrology applications it is crucial to understand the noise properties of this device. In this paper we present a detailed analysis of the intensity fluctuations by means of Monte-Carlo simulations and semi-classical approximations. We find that the light exhibits bunching below threshold, is to a good approximation coherent in the superradiant regime, and is chaotic above the second threshold.

Earth-alkaline-like atoms with ultra-narrow transitions open the door to a new regime of cavity quantum electrodynamics. That regime is characterized by a critical photon number that is many orders of magnitude smaller than what can be achieved in conventional systems. We show that it is possible to achieve superradiance in steady state with such systems. We discuss the basic underlying mechanisms as well as the key experimental requirements.

We present theoretical and experimental studies of the decoherence of hyperfine ground-state superpositions due to elastic Rayleigh scattering of light off-resonant with higher lying excited states. We demonstrate that under appropriate conditions, elastic Rayleigh scattering can be the dominant source of decoherence, contrary to previous discussions in the literature. We show that the elastic-scattering decoherence rate of a two-level system is given by the square of the difference between the elastic-scattering amplitudes for the two levels, and that for certain detunings of the light, the amplitudes can interfere constructively even when the elastic scattering rates from the two levels are equal. We confirm this prediction through calculations and measurements of the total decoherence rate for a superposition of the valence electron spin levels in the ground state of 9 Be + in a 4.5 T magnetic field.Off-resonant light scattering (spontaneous emission) is an important source of decoherence in many coherentcontrol experiments with atoms and molecules. Examples include the use of optical-dipole forces for gates in quantum computing [1], the generation of spin squeezed states through laser-mediated interactions [2][3][4][5][6], and the trapping and manipulation of neutral atoms in optical lattices [7,8]. These experiments frequently involve superpositions of two-level atomic systems (qubits) and use laser beams off-resonant with higher lying excited states to control and measure the atomic states.In general, decoherence of an atomic superposition state due to off-resonant light scattering occurs if the scattered photon carries information about the qubit state. During Raman scattering the initial and final qubit states differ. The state of the scattered photon is entangled with the atomic state, providing "welcherweg" (which-way) information and leading to decoherence [9,10]. By contrast the role of elastic Rayleigh scattering for decoherence is not as clear. Two very different regimes have been discussed and are supported by experiment. On the one hand it has been found that in some experiments Rayleigh scattering gives rise to negligible decoherence provided that the elastic scattering rates from both qubit levels are approximately equal [10]. On the other hand, decoherence due to Rayleigh scattering of photons on a cycling transition is used for strong projective state measurement [11].In this letter we develop a microscopic theory for the decoherence of a qubit due to elastic Rayleigh scattering that gives a unified treatment of these different regimes. Our key finding is that the decoherence induced by Rayleigh scattering is proportional to the square of the * Electronic address: huys@csir.co.za † Electronic address: john.bollinger@nist.gov difference of the probability amplitudes for elastic scattering from the two levels [Eq. (7)]. When the two amplitudes are approximately equal the resulting decoherence rate can be small (first case above) and when one amplitude dominates the other, Rayleigh decoherence c...

We consider the motion of the end mirror of a cavity in whose standing wave mode pattern atoms are trapped. The atoms and the light field strongly couple to each other because the atoms form a distributed Bragg mirror with a reflectivity that can be fairly high. We analyze how the dipole potential in which the atoms move is modified due to this backaction of the atoms. We show that the position of the atoms can become bistable. These results are of a more general nature and can be applied to any situation where atoms are trapped in an optical lattice inside a cavity and where the backaction of the atoms on the light field cannot be neglected. We analyze the dynamics of the coupled system in the adiabatic limit where the light field adjusts to the position of the atoms and the light field instantaneously and where the atoms move much faster than the mirror. We calculate the side band spectrum of the light transmitted through the cavity and show that these spectra can be used to detect the coupled motion of the atoms and the mirror.

We study an optomechanical system in which a microwave field and an optical field are coupled to a common mechanical resonator. We explore methods that use these mechanical resonators to store quantum mechanical states and to transduce states between the electromagnetic resonators from the perspective of the effect of mechanical decoherence. Besides being of fundamental interest, this coherent quantum state transfer could have important practical implications in the field of quantum information science, as it potentially allows one to overcome intrinsic limitations of both microwave and optical platforms. We discuss several state transfer protocols and study their transfer fidelity using a fully quantum mechanical model that utilizes quantum state-diffusion techniques. This work demonstrates that mechanical decoherence should not be an insurmountable obstacle in realizing high fidelity storage and transduction.

We describe a qualitatively new regime of cavity quantum electrodynamics, the super-strong coupling regime. This regime is characterized by atom-field coupling strengths of the order of the free spectral range of the cavity, resulting in a significant change in the spatial mode functions of the light field. It can be reached in practice for cold atoms trapped in an optical dipole potential inside the resonator. We present a nonperturbative scheme that allows us to calculate the frequencies and linewidths of the modified field modes, thereby providing a good starting point for a quantization of the theory.PACS numbers: 42.50. Fx,42.50.Pq, A striking characteristic of cavity quantum electrodynamics (CQED) is the conceptual simplicity of the systems involved. Typically, photons in a single cavity mode interact with atoms with a very small relevant number of internal quantum states [1]. On the experimental side this simplicity leads to the precise control of most system parameters and to the laboratory realization of many idealized theoretical models and Gedankenexperiments. For example, strongly nonclassical states of the light field such as e.g. number states [2,3] can be created, the entanglement between light and atoms can be studied, and important questions related to the quantum measurement process can be addressed. Over the last two decades experimentalists further expanded the scope of CQED by achieving increasing control over the translational degrees of freedom of the atoms via laser cooling and other cooling schemes, and CQED also plays an important role in quantum information research.In the strong coupling regime of CQED the coherent interaction between a single atom and the light field, characterized by the Rabi frequency g, dominates over the decoherence processes induced by the coupling to the environment, and characterized by the spontaneous decay rate γ and the cavity damping rate κ, g > γ, κ.(1)In contrast to these three characteristic frequencies, whose relative role in CQED has been explored in great detail in the past, the role of the free spectral range ω FSR of the resonator has largely been ignored so far. However, if one could achieve experimental conditions such thatthe coupled atoms-cavity system would enter a qualitatively new regime. In this regime the coupling between atoms and light is strong already during one round trip in the resonator, which is in contrast to the conventional strong coupling regime where sufficiently strong coupling is achieved through recycling of the light by means of a high Q cavity. Because the spatial mode pattern inside the resonator is established during one round trip it is easy to see that in the super strong coupling limit the atoms can affect the spatial mode structure itself, and not just the occupation of the modes as is typically the case in conventional CQED. The reason why that regime has not been clearly identified in the past is that ω FSR = c/2L, where L is the resonator length, is under most circumstances much too large to lead to significant e...