Due to their high coherence, a laser is a ubiquitous tool in science. We show that by engineering the coupling between the gain medium and the laser cavity as well as the laser cavity and the output port, it is possible to eliminate most of the noise due to photons entering as well as leaving the laser cavity. Hence, it is possible to reduce the laser linewidth by a factor equal to the number of photons in the laser cavity below the standard quantum limit. We design and theoretically analyze a superconducting circuit that uses Josephson junctions, capacitors and inductors to implement a microwave laser, including the low-noise couplers that allow the design to surpass the standard quantum limit. Our proposal relies on the elements of superconducting quantum information, and thus is an example of how quantum engineering techniques can inspire us to re-imagine the limits of conventional quantum systems.
We investigate a new laser scheme by using Ramsey separated-field technique with bad cavity. By studying the linewidth of the stimulated-emission spectrum of this kind of laser inside the cavity, we find its linewidth is more than two orders of magnitude narrower than atomic natural linewidth, and it is far superior to that of conventional optical Ramsey method and any other available subnatural linewidth spectroscopy at present. Since any cavity related noise is reduced to cavity-pulling effect in bad cavity laser, this Ramsey laser provides the possibility of precision subnatural linewidth s…
I discuss the robustness of the pumped cavity dynamics against phase diffusion of the laser and conclude that opto-mechanical cooling has extreme sensitivity compared to laser cooling of atoms. Certain proposals of ground state opto-mechanical cooling by single cavity would require an unrealistic sharp laser linewidth or equivalently, a very low level of phase noise. A systematic way to cancel classical excess phase noise is the interferometric twin-cavity pumping, initiated for optically trapped macro-mirrors of future gravitational-wave detectors.
A continuous atom laser will almost certainly have a linewidth dominated by the effect of the atomic interaction energy, which turns fluctuations in the condensate atom number into fluctuations in the condensate frequency. These correlated fluctuations mean that information about the atom number could be used to reduce the frequency fluctuations, by controlling a spatially uniform potential. We show that feedback based on a physically reasonable quantum non-demolition measurement of the atom number of the condensate in situ can reduce the linewidth enormously.
We present a fully quantum mechanical treatment of a single mode atom laser including pumping and output coupling. By ignoring atom-atom interactions, we have solved this model without making the Born-Markov approximation. We find substantially less gain narrowing than is predicted under that approximation.
The standard quantum limit to the linewidth of a laser for which the gain medium can be adiabatically eliminated is $\ell_{0}=κ/2\bar{n}$. Here $κ$ is the intensity damping rate and $\bar{n}$ the mean photon number. This contains equal contributions from the loss and gain processes, so that simple arguments which attribute the linewidth wholly to phase noise from spontaneous gain are wrong. I show that an {\em unstimulated} gain process actually introduces no phase noise, so that the ultimate quantum limit to the laser linewidth comes from the loss alone and is equal to $\ell_{ult}= κ/4\bar{n}…
We propose a solid-state based superradiance laser which is almost insensitive to the cavity mirror vibration. Therefore, it can compete with the best frequency-stable local oscillators. The long coherence time and the large optical density of rare-earth-ions (REIs) doped solids are employed to find a regime to demonstrate a steady-state laser emission with linewidth smaller than the atomic decay rate. The experimental parameters are discussed and intracavity photon number and laser linewidth are calculated based on the mean-field theory. A procedure for measuring absolute laser linewidth is p…
In this tutorial, the physical origins and mathematical analyses of laser linewidths are reviewed. The semi-classical model is based on an equation for the light-mode amplitude that includes random source terms, one term for each process that affects the amplitude (stimulated and spontaneous emission, stimulated absorption, and facet and material loss). Although the source terms are classical, their assigned strengths are consistent with the laws of quantum optics. Analysis of this equation shows that the laser linewidth is proportional to the sum of the (positive) source strengths for all gai…
The problem of the quantum-limited or intrinsic linewidth of a good-cavity laser is revisited. Starting from the Scully-Lamb master equation, we present a fully analytical treatment to determine the correlation function and the spectrum of the cavity field at steady state. For this purpose, we develop an analytical approximation method that implicitly incorporates the microscopic fluctuations of both the phase and intensity of the field, and, in addition, takes full account of the saturation of the nonlinear gain. Our main result is a simple formula for the quantum-limited linewidth that is va…
We discuss the use of electromagnetically modified absorption to achieve selective excitation in atoms: that is, the laser excitation of one transition while avoiding simultaneously exciting another transition whose frequency is the same as or close to that of the first. The selectivity which can be achieved in the presence of electromagnetically induced transparency (EIT) is limited by the decoherence rate of the dark state. We present exact analytical expressions for this effect, and also physical models and approximate expressions which give useful insights into the phenomena. When the lase…
We investigate the linewidth of a quasi-continuous atom laser within a semiclassical framework. In the high flux regime, the lasing mode can exhibit a number of undesirable features such as density fluctuations. We show that the output therefore has a complicated structure that can be somewhat simplified using Raman outcoupling methods and energy-momentum selection rules. In the weak outcoupling limit, we find that the linewidth of an atom laser is instantaneously Fourier limited, but, due to the energy `chirp' associated with the draining of a condensate, the long-term linewidth of an atom la…
We investigate theoretically the influence of laser phase noise on the cooling and heating of a generic cavity optomechanical system. We derive the back-action damping and heating rates and the mechanical frequency shift of the radiation pressure-driven oscillating mirror, and derive the minimum phonon occupation number for small laser linewidths. We find that in practice laser phase noise does not pose serious limitations to ground state cooling. We then consider the effects of laser phase noise in a parametric cavity driving scheme that minimizes the back-action heating of one of the quadrat…
The linewidth of an atom laser can be limited by excitation of higher energy modes in the source Bose-Einstein condensate, energy shifts in that condensate due to the atomic interactions, or phase diffusion of the lasing mode due to those interactions. The first two are effects that can be described with a semiclassical model, and have been studied in detail for both pumped and unpumped atom lasers. The third is a purely quantum statistical effect, and has been studied only in zero dimensional models. We examine an unpumped atom laser in one dimension using a quantum field theory using stochas…
We propose a new type of superradiant laser based on a hot atomic beam traversing an optical cavity. We show that the theoretical minimum linewidth and maximum power are competitive with the best ultracoherent clock lasers. Also, our system operates naturally in continuous wave mode, which has been elusive for superradiant lasers so far. Unlike existing ultracoherent lasers, our design is simple and rugged. This makes it a candidate for the first widely accessible ultracoherent laser, as well as the first to realize sought-after applications of ultracoherent lasers in challenging environments.
We report on the implementation of a high fidelity universal gate-set on optical qubits based on trapped $^{88}$Sr$^+$ ions for the purpose of quantum information processing. All coherent operations were performed using a narrow linewidth diode laser. We employed a master-slave configuration for the laser, where an ultra low expansion glass (ULE) Fabry-Perot cavity is used as a stable reference as well as a spectral filter. We characterized the laser spectrum using the ions with a modified Ramsey sequence which eliminated the affect of the magnetic field noise. We demonstrated high fidelity si…
It is known that cross-correlation between the random intensity fluctuations of two lasers forming electromagnetically-induced transparency (EIT) exhibits a transition from correlation to anticorrelation. We study the linewidth behavior of this transition and have found the linewidth is below the (effective) coherence lifetime limit and is only limited by competing noises. We established a numerical model which reveals the linewidth dependence on laser linewidth and laser power. Our experiments using lasers with different linewidth showed results in qualitative agreement with the model. This r…
In recent years, many peculiar sensors have been proposed, such as the sensors based on exceptional points, Parity-Time symmetric structures or non-reciprocal systems. It is crucial to evaluate the fundamental limit of these sensing schemes and to judge whether there is an enhanced performance. Several papers have already investigated the fundamental limits based on different aspects and criteria, some led to different conclusions. In this paper, we suggest that for linear bosonic sensors that can be modeled as coupled oscillators below threshold, a measurement of the mode frequency $w_0$ can …
The elastic scattering peak of a resonantly driven two-level system has been argued to provide narrow-linewidth antibunched photons. Although independent measurements of spectral width on the one hand and antibunching on the other hand do seem to show that this is the case, a joint measurement reveals that only one or the other of these attributes can be realised in the direct emission. We discuss a scheme which interferes the emission with a laser to produce simultaneously single photons of subnatural linewidth. In particular, we consider the effect of dephasing and of the detuning between th…
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.
A continuous wave atom laser formed by the outcoupling of atoms from a trapped Bose-Einstein condensate (BEC) potentially has a range of metrological applications. However, in order for the device to be truly continuous, a mechanism to replenish the atoms in the BEC is required. Here we calculate the temporal coherence properties of a continuously pumped atom laser beam outcoupled from a trapped Bose-Einstein condensate which is replenished from a reservoir at finite temperature. We find that the thermal fluctuations of the condensate can significantly decrease the temporal coherence of the ou…
We report on the development of a diode laser system - the `Faraday laser' - using an atomic Faraday filter as the frequency-selective element. In contrast to typical external-cavity diode laser systems which offer tunable output frequency but require additional control systems in order to achieve a stable output frequency, our system only lases at a single frequency, set by the peak transmission frequency of the internal atomic Farady filter. Our system has both short-term and long-term stability of less than 1~MHz, which is less than the natural linewidth of alkali-atomic D-lines, making sim…
Nanocavity lasers are commonly characterized by the spontaneous coupling coefficient $β$ that represents the fraction of photons emitted into the lasing mode. While $β$ is conventionally discussed in semiconductor lasers where the photon lifetime is much shorter than the carrier lifetime (class-B lasers), little is known about $β$ in atomic lasers where the photon lifetime is much longer than the other lifetimes and only the photon degree of freedom exists (class-A lasers). We investigate the impact of the spontaneous coupling coefficient $β$ on lasing properties in the class-A limit by extend…
A random-matrix theory is presented for the linewidth of a laser cavity in which the radiation is scattered chaotically. The linewidth is enhanced above the Schawlow-Townes value by the Petermann factor K, due to the non-orthogonality of the cavity modes. The factor K is expressed in terms of a non-Hermitian random matrix and its distribution is calculated exactly for the case that the cavity is coupled to the outside via a small opening. The average of K is found to depend non-analytically on the area of the opening, and to greatly exceed the most probable value.
Today's best atomic clocks are limited by frequency noise on the lasers used to interrogate the atoms. A proposed solution to this problem is to create a superradiant laser using an optical clock transition as its gain medium. This laser would act as an active atomic clock, and would be highly immune to the fluctuations in reference cavity length that limit today's best lasers. Here, we demonstrate and characterize superradiant emission from the mHz linewidth clock transition in an ensemble of laser-cooled $^{87}$Sr atoms trapped within a high-finesse optical cavity. We measure a collective en…
We present a quantum-mechanical treatment of the coherence properties of a single-mode atom laser. Specifically, we focus on the quantum phase noise of the atomic field as expressed by the first-order coherence function, for which we derive analytical expressions in various regimes. The decay of this function is characterized by the coherence time, or its reciprocal, the linewidth. A crucial contributor to the linewidth is the collisional interaction of the atoms. We find four distinct regimes for the linewidth with increasing interaction strength. These range from the standard laser linewidth…
The linewidth enhancement factor (LEF) describes the coupling between amplitude and phase fluctuations in a semiconductor laser, and has recently been shown to be a crucial component for frequency comb formation in addition to linewidth broadening. It necessarily arises from causality, as famously formulated by the Kramers-Kronig relation, in media with non-trivial dependence of the susceptibility on intensity variations. While thermal contributions are typically slow, and thus can often be excluded by suitably designing the dynamics of an experiment, the many quantum contributions are harder …
Diode laser self-injection locking (SIL) to a whispering gallery mode of a high quality factor resonator is a widely used method for laser linewidth narrowing and high-frequency noise suppression. SIL has already been used for the demonstration of ultra-low-noise photonic microwave oscillators and soliton microcomb generation and has a wide range of possible applications. Up to date, SIL was demonstrated only with a single laser. However, multi-frequency and narrow-linewidth laser sources are in high demand for modern telecommunication systems, quantum technologies, and microwave photonics. He…
We demonstrate a novel approach to obtain resonance linewidth below that limited by coherence lifetime. Cross correlation between induced intensity modulation of two lasers coupling the target resonance exhibits a narrow spectrum. 1/30 of the lifetime-limited width was achieved in a proof-of-principle experiment where two ground states are the target resonance levels. Attainable linewidth is only limited by laser shot noise in principle. Experimental results agree with an intuitive analytical model and numerical calculations qualitatively. This technique can be easily implemented and should be…
