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Virtual excitations, inherent to ultrastrongly coupled light-matter systems, induce measurable modifications in system properties, offering a novel resource for quantum technologies. In this work, we demonstrate how these virtual excitations and their correlations can be harnessed to enhance precision measurements, without the need to extract them. Building on the paradigmatic Dicke model, which describes the interaction between an ensemble of two-level atoms and a single radiation mode, we propose a method to harness hybridized light-matter modes for quantum metrology. Our results not only highlight the potential of virtual excitations to surpass classical precision limits but also extend to a broad range of ultrastrongly coupled systems., Comment: 6 + 4 pages, 3 + 3 figures

Due to the inherently probabilistic nature of quantum mechanics, each experimental realization of a dynamical quantum system may yield a different measurement outcome, especially when the system is coupled to an environment that causes dissipation. Although it is in principle possible that some quantum trajectories lead to exotic highly entangled quantum states, the probability of observing these trajectories is usually extremely low. In this work, we show how to maximize the probability of generating highly entangled states, including maximally entangled cat states, in an ensemble of atoms experiencing superradiant decay. To this end, we analyze an effective non-Hermitian Hamiltonian which governs the dynamics between the quantum jumps associated with photon emission. A key result of our study is that, in order to maximally enhance the probability of cat state generation, the initial state needs to be non-classical. This can be achieved e.g. with one-axis twisting in a cavity-QED system., Comment: 7+2 pages, 6+2 color figures

We demonstrate the possibility of reconstructing images from fNIRS brain activity and start building a prototype to match the required specs. By training an image reconstruction model on downsampled fMRI data, we discovered that cm-scale spatial resolution is sufficient for image generation. We obtained 71% retrieval accuracy with 1-cm resolution, compared to 93% on the full-resolution fMRI, and 20% with 2-cm resolution. With simulations and high-density tomography, we found that time-domain fNIRS can achieve 1-cm resolution, compared to 2-cm resolution for continuous-wave fNIRS. Lastly, we share designs for a prototype time-domain fNIRS device, consisting of a laser driver, a single photon detector, and a time-to-digital converter system.

In contrast to free space, in waveguides the dispersive and dissipative dipole-dipole interactions among quantum emitters exhibit a periodic behavior over remarkably long distances. We propose a novel setup exploiting this long-range periodicity in order to create highly excited subradiant states and facilitate fast controlled collective energy transport amongst far-apart ensembles coupled to a waveguide. For sufficiently large ensembles collective superradiant emission into the fiber modes dominates over its free space counterpart. We show that for a large number of emitters a fast transverse coherent pulse can create almost perfect subradiant states with up to $50\%$ excitation. On the other hand, for a coherent excitation of one sub-ensemble above an overall excitation fraction of $50\%$ we find a nearly lossless and fast energy transfer to the ground state sub-ensemble. This transport can be enhanced or suppressed by controlling the positions of the ensembles relative to each other, while it can also be realized with a random position distribution. In the optimally enhanced case this fast transfer appears as superradiant emission with subsequent superabsorption, yet, without a superradiant decay after the absorption. The highly excited subradiant states as well as the superradiant excitation transfer appear as suitable building blocks in applications like active atomic clocks, quantum batteries, quantum information protocols and quantum metrology procedures such as fiber-based Ramsey schemes., Comment: 9 pages, 7 figures

Critical metrology relies on the precise preparation of a system in its ground state near a quantum phase transition point where quantum correlations get very strong. Typically this increases the quantum Fisher information with respect to changes in system parameters and thus improves the optimally possible measurement precision limited by the Cram\'er-Rao bound. Hence critical metrology involves encoding information about the unknown parameter in changes of the system's ground state. Conversely, in conventional metrology methods like Ramsey interferometry, the eigenstates of the system remain unchanged, and information about the unknown parameter is encoded in the relative phases that excited system states accumulate during their time evolution. Here we introduce an approach combining these two methodologies into a unified protocol applicable to closed and driven-dissipative systems. We show that the quantum Fisher information in this case exhibits an additional interference term originating from the interplay between eigenstate and relative phase changes. We provide analytical expressions for the quantum and classical Fisher information in such a setup, elucidating as well a straightforward measurement approach that nearly attains the maximum precision permissible under the Cram\'er-Rao bound. We showcase these results by focusing on the squeezing Hamiltonian, which characterizes the thermodynamic limit of Dicke and Lipkin-Meshkov-Glick Hamiltonians., Comment: 6 pages, 3 figures

Recent theoretical predictions hint at an implementation of a superradiant laser based on narrow optical clock transitions by using a filtered thermal beam at high density. Corresponding numerical studies give encouraging results but the required very high densities are sensitive to beam collimation errors and inhomogeneous shifts. Here we present extensive numerical studies of threshold conditions and the predicted output power of such a superradiant laser involving realistic particle numbers and velocities along the cavity axis. Detailed studies target the threshold scaling as a function of temperature as well as the influence of eliminating the hottest part of the atomic distribution via velocity filtering and the benefits of additional atomic beam guiding. Using a cumulant expansion approach allows us to quantify the significance of atom-atom and atom-field correlations in such configurations. We predict necessary conditions to achieve a certain threshold photon number depending on the atomic temperature and density. In particular, we show that the temperature threshold can be significantly increased by using more atoms. Interestingly, a velocity filter removing very fast atoms has only almost negligible influence despite their phase perturbing properties. On the positive side an additional conservative optical guiding towards cavity mode antinodes leads to significantly lower threshold and higher average photon number. Interestingly we see that higher order atom-field and direct atom-atom quantum correlations play only a minor role in the laser dynamics, which is a bit surprising in the superradiant regime., Comment: 12 pages, 6 figures

When an inverted ensemble of atoms is tightly packed on the scale of its emission wavelength or when the atoms are collectively strongly coupled to a single cavity mode, their dipoles will align and decay rapidly via a superradiant burst. However, a spread-out dipole phase distribution theory predicts a required minimum threshold of atomic excitation for superradiance to occur. Here we experimentally confirm this predicted threshold for superradiant emission on a narrow optical transition when exciting the atoms transversely and show how to take advantage of the resulting sub- to superradiant transition. A $\pi/2$-pulse places the atoms in a subradiant state, protected from collective cavity decay, which we exploit during the free evolution period in a corresponding Ramsey pulse sequence. The final excited state population is read out via superradiant emission from the inverted atomic ensemble after a second $\pi/2$-pulse, and with minimal heating this allows for multiple Ramsey sequences within one experimental cycle. Our scheme is a fundamentally new approach to atomic state readout characterized by its speed, simplicity, and high sensitivity. It demonstrates the potential of sensors using collective effects in cavity-coupled quantum emitters., Comment: Removed a duplicate paragraph

Squeezing is essential to many quantum technologies and our understanding of quantum physics. Here we develop a theory of steady-state squeezing that can be generated in the closed and open quantum Rabi as well as Dicke model. To this end, we eliminate the spin dynamics which effectively leads to an abstract harmonic oscillator whose eigenstates are squeezed with respect to the physical harmonic oscillator. The generated form of squeezing has the unique property of time-independent uncertainties and squeezed dynamics, a novel type of quantum behavior. Such squeezing might find applications in continuous back-action evading measurements and should already be observable in optomechanical systems and Coulomb crystals., Comment: 9 pages, 3 figures

Ramsey spectroscopy in large, dense ensembles of ultra-cold atoms trapped in optical lattices suffers from dipole-dipole interaction induced shifts and collective superradiance limiting its precision and accuracy. We propose a novel geometry implementing fast signal readout with minimal heating for large atom numbers at lower densities via an optical cavity operated in the weak single atom but strong collective coupling regime. The key idea is controlled collective transverse $\pi/2$-excitation of the atoms to prepare a macroscopic collective spin protected from cavity superradiance. This requires that the two halves of the atomic ensemble are coupled to the cavity mode with opposite phase, which is naturally realized for a homogeneously filled volume covering odd and even sites of the cavity mode along the cavity axis. The origin of the superior precision can be traced back to destructive interference among sub-ensembles in the complex nonlinear collective atom field dynamics. In the same configuration we find surprising regular self-pulsing of the cavity output for suitable continuous illumination. Our simulations for large atom numbers employing a cumulant expansion are qualitatively confirmed by a full quantum treatment of smaller ensembles., Comment: 8 pages, 7 figures

A suitable scheme to continuously create inversion on an optical clock transition with negligible perturbation is a key missing ingredient required to build an active optical atomic clock. Re- pumping of the atoms on the narrow transition typically needs several pump lasers in a multi step process involving several auxiliary levels. In general this creates large effective level shifts and a line broadening, strongly limiting clock accuracy. Here we present an extensive theoretical study for a realistic multi-level implementation in search of parameter regimes where a sufficient inversion can be achieved with minimal perturbations. Fortunately we are able to identify a useful operating regime, where the frequency shifts remain small and controllable, only weakly perturbing the clock transition for useful pumping rates. For practical estimates of the corresponding clock performance we introduce a straightforward mapping of the multilevel pump scheme to an effective energy shift and broadening parameters for the reduced two-level laser model system. This allows to evaluate the resulting laser power and spectrum using well-known methods.

Theoretical studies of superradiant lasing on optical clock transitions predict a superb frequency accuracy and precision closely tied to the bare atomic linewidth. Such a superradiant laser is also robust against cavity fluctuations when the spectral width of the lasing mode is much larger than that of the atomic medium. Recent predictions suggest that this unique feature persists even for a hot and thus strongly broadened ensemble, provided the effective atom number is large enough. Here we use a second-order cumulant expansion approach to study the power, linewidth and lineshifts of such a superradiant laser as a function of the inhomogeneous width of the ensemble including variations of the spatial atom-field coupling within the resonator. We present conditions on the atom numbers, the pump and coupling strengths required to reach the buildup of collective atomic coherence as well as scaling and limitations for the achievable laser linewidth., Comment: 9 pages, 9 figures

A full quantum mechanical treatment of open quantum systems via a Master equation is often limited by the size of the underlying Hilbert space. As an alternative, the dynamics can also be formulated in terms of systems of coupled differential equations for operators in the Heisenberg picture. This typically leads to an infinite hierarchy of equations for products of operators. A well-established approach to truncate this infinite set at the level of expectation values is to neglect quantum correlations of high order. This is systematically realized with a so-called cumulant expansion, which decomposes expectation values of operator products into products of a given lower order, leading to a closed set of equations. Here we present an open-source framework that fully automizes this approach: first, the equations of motion of operators up to a desired order are derived symbolically using predefined canonical commutation relations. Next, the resulting equations for the expectation values are expanded employing the cumulant expansion approach, where moments up to a chosen order specified by the user are included. Finally, a numerical solution can be directly obtained from the symbolic equations. After reviewing the theory we present the framework and showcase its usefulness in a few example problems.

Simultaneous strong coherent pumping of the two transitions of a V-level atom with very differentdecay rates has been predicted to create almost perfect inversion on the narrower transition. Usingthe example of the blue and red transitions in Strontium we show that for suitable operatingconditions the corresponding resonant gain can be used to continuously operate a laser on thenarrow transition. In particular, for a strong detuning of the pump field with respect to the narrowtransition, coherent laser emission occurs close to the bare atomic transition frequency exhibitingonly a negligible contribution from coherent pump light scattered into the lasing mode.Calculations of the cavity output spectrum show that the resulting laser linewidth can get muchsmaller than the bandwidth of the pump light and even the natural linewidth of the narrow atomictransition. Its frequency is closely tied to the atomic transition frequency for properly chosen atomnumbers. Simulations including atomic motionshow Doppler cooling on the strong transitionwith minor motion heating on the lasing transition, so that continuous laser operation in thepresence of a magneto-optical trap should be possible with current experimental technology.

A cold atomic gas with an inverted population on a transition coupled to a field mode of an optical resonator constitutes a generic model of a laser. For quasi-continuous operation, external pumping, trapping and cooling of the atoms is required to confine them in order to achieve enough gain inside the resonator. As inverted atoms are high-field seekers in blue detuned light fields, tuning the cavity mode to the blue side of the atomic gain transition allows for combining lasing with stimulated cavity cooling and dipole trapping of the atoms at the antinodes of the laser field. We study such a configuration using a semiclassical description of particle motion along the cavity axis. In extension of earlier work we include free space atomic and cavity decay as well as atomic dipole-dipole interactions and their corresponding forces. We show that for a proper choice of parameters even in the bad cavity limit the atoms can create a sufficiently strong field inside the resonator such that they are trapped and cooled via the superradiant lasing action with less than one photon on average inside the cavity.