Within the new description of the polarization structure of quantum light (given in Part I) some types of generalized coherent states related to the polarization SU(2) group are examined. With their help we give a quasiclassical description of polarization properties of light fields and discuss the concept of squeezing and uncertainty relations for multimode light in the polarization quantum optics. As a consequence, a new classification of polarization states of quantum light is obtained. We also derive geometric phases acquired by different quantum light beams transmitted through "polarization rotators".
We study polarization squeezing of a light beam initially in the coherent state using the nonlinear interaction hamiltonian $ H=k\big(\hat a_{x}^{\dagger2}+{\hat a_{x}}^2\big)$. For the degree of polarization squeezing, we use a definition written in the final form by the authors and also used in earlier papers. We find that the polarization squeezing can be very high and the degree of polarization squeezing can be less than unity by a very small amount. We achieve the polarization squeezing even for very low beam intensity under some conditions involving phase angles in the polarization modes…
We report on a novel and efficient source of polarization squeezing using a single pass through an optical fiber. Simply passing this Kerr squeezed beam through a carefully aligned lambda/2 waveplate and splitting it on a polarization beam splitter, we find polarization squeezing of up to 5.1 +/- 0.3 dB. The experimental setup allows for the direct measurement of the squeezing angle.
Polarization squeezing is shown to occur in non-degenerate parametric amplification of coherent light and the degree of squeezing at interaction time $T$ can be as large as $1-e^{-2T}$. This gives $86.4\%$ polarization squeezing for $T=1$ and $98.2\%$ for $T=2$. One simple case when this occurs is on taking initially plane polarized light having equal amplitudes in the two modes that finally has equal intensities of two circular polarizations. This suggest the experimental settings of parameters to achieve this extent of polarization squeezing in coherent light.
The dynamic feature of monochromatic bi-modal chaotic optical field, enriched with orthogonally-polarized basis-modes propagating collinearly and undergoing Degenerate Parametric Amplification, is investigated to demonstrate Squeezing in Hidden Optical-Polarization states. The Variance (Noise) of Hidden Optical-Polarization Parameters showing squeezing therein is numerically studied by identifying a Squeezing - Function. This squeezing in HOPS is seen to depend critically on interaction time and an Onset-time responsible for the same is demarcated.
The impact of the operator-valued commutator on nonclassical properties of continuous polarization variables is discussed. The definition of polarization squeezing is clarified to exclude those squeezed states which do not contain any new physics beyond quadrature squeezing. We present a consistent derivation of the general nonseparability criterion for the continuous variables with the operator-valued commutator, and apply it to the polarization variables.
We consider the superpositions of spin coherent states and study the coherence properties and spin squeezing in these states. The spin squeezing is examined using a new version of spectroscopic squeezing criteria. The results show that the antibuching effect can be enhanced and spin squeezing can be generated in the superpositions of two spin coherent states.
Photonic Crystal Fibers can be tailored to increase the effective Kerr nonlinearity, while producing smaller amounts of excess noise compared to standard silicon fibers. Using these features of Photonic Crystal Fibers we create polarization squeezed states with increased purity compared to standard fiber squeezing experiments. Explicit we produce squeezed states in counter propagating pulses along the same fiber axis to achieve near identical dispersion properties. This enables the production of polarization squeezing through interference in a polarization type Sagnac interferometer. We observ…
We report an interaction that controls spin squeezing in a collection of spin 1/2 particles. We describe how spin squeezing can be generated and maintained in time. Our scheme can be applied to control the spin squeezing in a Bose condensate with two internal spin states.
A 2.8-dB polarization squeezing of the Stokes operator S2 for the rubidium D1 line (795 nm) is achieved, with the lowest squeezing band at an audio frequency of 2.6 kHz. Two methods are applied for improving the squeezing towards low frequencies: an orthogonal-polarized locking beam that precludes residual unwanted interference and quantum noise locking method that stabilizes the relative phase between the squeezed vacuum and the local oscillator. The squeezing level is limited by absorption-induced losses at short wavelengths, here is 397.5 nm. The generated polarization squeezed light can be…
We show that it is possible to generate continuous-wave fields and pulses of polarization squeezed light by sending classical, linearly polarized laser light twice through an atomic sample which causes an optical Faraday rotation of the field polarization. We characterize the performance of the process, and we show that an appreciable degree of squeezing can be obtained under realistic physical assumptions.
We introduce the nonlinear spin coherent state via its ladder operator formalism and propose a type of nonlinear spin coherent state by the nonlinear time evolution of spin coherent states. By a new version of spectroscopic squeezing criteria we study the spin squeezing in both the spin coherent state and nonlinear spin coherent state. The results show that the spin coherent state is not squeezed in the x, y, and z directions, and the nonlinear spin coherent state may be squeezed in the x and y directions.
We report on the generation of polarization squeezing of intense, short light pulses using an asymmetric fiber Sagnac interferometer. The Kerr nonlinearity of the fiber is exploited to produce independent amplitude squeezed pulses. The polarization squeezing properties of spatially overlapped amplitude squeezed and coherent states are discussed. The experimental results for a single amplitude squeezed beam are compared to the case of two phase-matched, spatially overlapped amplitude squeezed pulses. For the latter, noise variances of -3.4dB below shot noise in the S0 and the S1 and of -2.8dB i…
We study the interaction of a nearly resonant linearly polarized laser beam with a cloud of cold cesium atoms in a high finesse optical cavity. We show theoretically and experimentally that the cross-Kerr effect due to the saturation of the optical transition produces quadrature squeezing on both the mean field and the orthogonally polarized vacuum mode. An interpretation of this vacuum squeezing as polarization squeezing is given and a method for measuring quantum Stokes parameters for weak beams via a local oscillator is developed.
We present a theoretical study of an ensemble of X-like 4-level atoms placed in an optical cavity driven by a linearly polarized field. We show that the self-rotation (SR) process leads to polarization switching (PS). Below the PS threshold, both the mean field mode and the orthogonal vacuum mode are squeezed. We provide a simple analysis of the phenomena responsible for the squeezing and trace the origin of vacuum squeezing not to SR, but to crossed Kerr effect induced by the mean field. Last, we show that this vacuum squeezing can be interpreted as polarization squeezing.
The U(2) invariant approach is delineated for the pair coherent states to explore their squeezing properties. This approach is useful for a complete analysis of the squeezing properties of these two-mode states. We use the maximally compact subgroup U(2) of Sp(4,R) to mix the modes, thus allowing us to search over all possible quadratures for squeezing. The variance matrix for the pair coherent states turns out to be analytically diagonalisable, giving us a handle over its least eigenvalue, through which we are able to pin down the squeezing properties of these states. In order to explicitly d…
We analyze effects of squeezing upon superpositions of coherent states (SCSs) and entangled coherent states (ECSs) for Bell-inequality tests. We find that external squeezing can always increase the degrees of Bell violations, if the squeezing direction is properly chosen, for the case of photon parity measurements. On the other hand, when photon on/off measurements are used, the squeezing operation can enhance the degree of Bell violations only for moderate values of amplitudes and squeezing. We point out that a significant improvement is required over currently available squeezed SCSs in orde…
A particularly simple setup is introduced to study the influence of time-delayed coherent feedback on the optical squeezing properties of the degenerate parametric amplifier (DPA). The possibility for significantly enhanced squeezing is demonstrated both on resonance and in sidebands, at a reduced pump power compared to the case without feedback. We study a broad range of operating parameters and their influence on the characteristic squeezing of the system. A classical analysis of the system dynamics reveals the connection between the feedback-modified landscape of stability and enhanced sque…
Coherence has been remaining a key resource for numerous applications of quantum physics ranging from quantum metrology to quantum information. Here, we report a theoretical work on how maximally created coherence results in the squeezing of cavity field coupled to a coherently driven single quantum dot. We employ a recently developed polaron master equation theory for accurately incorporating the impact of exciton-phonon coupling on squeezing.
We further elaborate the theory of quantum fluctuations in vertical-cavity surface-emitting lasers (VCSELs), developed in Ref. \cite{Hermier02}. In particular, we introduce the quantum Stokes parameters to describe the quantum self- and cross-correlations between two polarization components of the electromagnetic field generated by this type of lasers. We calculate analytically the fluctuation spectra of these parameters and discuss experiments in which they can be measured. We demonstrate that in certain situations VCSELs can exhibit polarization squeezing over some range of spectral frequenc…
We discuss the possibility of generating noncritical quadrature squeezing by spontaneous polarization symmetry breaking. We consider first type-II frequency-degenerate optical parametric oscillators, but discard them for a number of reasons. Then we propose a four-wave mixing cavity in which the polarization of the output mode is always linear but has an arbitrary orientation. We show that in such a cavity complete noise suppression in a quadrature of the output field occurs, irrespective of the parameter values.
We have examined both single and entangled two-mode multiphoton coherent states and shown how the `Janus-faced' properties between two partner states are mirrored in appropriate tomograms. Entropic squeezing, quadrature squeezing and higher-order squeezing properties for a wide range of nonclassical states are estimated directly from tomograms. We have demonstrated how squeezing properties of two-mode entangled states produced at the output port of a quantum beamsplitter are sensitive to the relative phase between the reflected and transmitted fields. This feature allows for the possibility of…
We have analyzed the quadrature squeezing in a cavity mode driven by coherent light and interacting with a two-level atom. We have found that the cavity mode is in a squeezed state, with the maximum quadrature squeezing being $50\%$ below the vacuum-state level. We have also considered the superposition of a pair of cavity modes, each driven by coherent light and interacting with a two-level atom. We have found that the superposed cavity modes are in a squeezed state and the squeezing occurs in both quadratures. We have established that the uncertainty relation perfectly holds for this case. I…
We report on nonlinear squeezing effects of polarization states of light by harnessing the intrinsic correlations from a polarization-entangled light source and click-counting measurements. Nonlinear Stokes operators are obtained from harnessing the click-counting theory in combination with angular-momentum-type algebras. To quantify quantum effects, theoretical bounds are derived for second- and higher-order moments of nonlinear Stokes operators. The experimental validation of our concept is rendered possible by developing an efficient source, using a spectrally decorrelated type-II phase-mat…
We observed squeezed vacuum light at 795 nm in 87Rb vapor via resonant polarization self-rotation, and report noise sidebands suppression of ~1 dB below shot noise level spanning from acoustic (30 kHz) to MHz frequencies. This is the first demonstration of sub-MHz quadrature vacuum squeezing in atomic systems. The spectral range of observed squeezing matches well typical bandwidths of electromagnetically induced transparency (EIT) resonances, making this simple technique for generation of optical fields with non-classical statistics at atomic transitions wavelengths attractive for EIT-based qu…
We show that high squeezing and entanglement can be generated at the output of a cavity containing atoms interacting with two fields in a Coherent Population Trapping situation, on account of a non-linear Faraday effect experienced by the fields close to a dark-state resonance in a cavity. Moreover, the cavity provides a feedback mechanism allowing to reduce the quantum fluctuations of the ground state spin, resulting in strong steady state spin-squeezing.
We consider a resonant bichromatic excitation of N trapped ions that generates displacement and squeezing in their collective motion conditioned to their ionic internal state, producing eventually Scrhodinger cat states and entangled squeezing. Furthermore, we study the case of tetrachromatic illumination or producing the so called entangled coherent states in two motional normal modes.
We theoretically study quadrature and polarization squeezing in dispersive optical bistability through a vectorial Kerr cavity model describing a nonlinear cavity filled with an isotropic chi(3) medium in which self-phase and cross-phase modulation, as well as four--wave mixing, occur. We derive expressions for the quantum fluctuations of the output field quadratures as a function of which we express the spectrum of fluctuations of the output field Stokes parameters. We pay particular attention to study how the bifurcations affecting the non-null linearly polarized output mode squeezes the ort…
We report the first direct experimental characterization of continuous variable quantum Stokes parameters. We generate a continuous wave light beam with more than 3 dB of simultaneous squeezing in three of the four Stokes parameters. The polarization squeezed beam is produced by mixing two quadrature squeezed beams on a polarizing beam splitter. Depending on the squeezed quadrature of these two beams the quantum uncertainty volume on the Poincaré sphere became a `cigar' or `pancake'-like ellipsoid.
We analyze theoretically a scheme that produces spin squeezing via the continuous swapping of atom-photon entanglement into atom-atom entanglement, and propose an explicit experimental system where the necessary atom-field coupling can be realized. This scheme is found to be robust against perturbations due to other atom-field coupling channels.
Coherent feedback is a non-measurement based, hence a back-action free, method of control for quantum systems. A typical application of this control scheme is squeezing enhancement, a purely non-classical effect in quantum optics. In this paper we report its first experimental demonstration that well agrees with the theory taking into account time delays and losses in the coherent feedback loop. The results clarify both the benefit and the limitation of coherent feedback control in a practical situation.
We study relations between bosonic quadrature squeezing and atomic spin squeezing, and find that the latter reduces to the former in the limit of a large number of atoms for even and odd states. We demonstrate this reduction by treating even and odd spin coherent states, for which analytical solutions are readily obtained, and prove that even spin coherent states always exhibit spin squeezing, whereas odd spin coherent states do not, analogous to the squeezing characteristic of even and odd bosonic coherent states. Finally, we examine the squeezing transfer between photons and atoms via the Di…
We propose a theoretical method to enhance the coherent dipole coupling between two atoms in an optical cavity via parametrically squeezing the cavity mode. In the present scheme, conditions for coherent coupling are derived in detail and diverse dynamics of the system can be obtained by regulating system parameters. In the presence of environmental noise, an auxiliary squeezed field is employed to suppress, and even completely eliminate the additional noise induced by squeezing. In addition, we demonstrate that our scheme enables the effective suppression of atomic spontaneous emission. The r…
We study polarization squeezing of a pure photon number state which is obviously polarized but the mere change in the basis of polarization leads to simultaneous polarization squeezing in all the components of Stokes operator vector except those falling along or perpendicular to the direction of polarization state, is observed. We use the most general definition of polarization squeezing and discuss the experimental feasibility of the result. We also observe that a squeezing operation like non-degenerate parametric amplification of the state does not reveal simultaneous squeezing in all Stokes…
Quantum coherent feedback control is a measurement-free control method fully preserving quantum coherence. In this paper we show how time-delayed quantum coherent feedback can be used to control the degree of squeezing in the output field of a cavity containing a degenerate parametric oscillator. We focus on the specific situation of Pyragas-type feedback control where time-delayed signals are fed back directly into the quantum system. Our results show how time-delayed feedback can enhance or decrease the degree of squeezing as a function of time delay and feedback strength.
We propose a new method of spin squeezing of atomic spin, based on the interactions between atoms and off-resonant light which are known as paramagnetic Faraday rotation and fictitious magnetic field of light. Since the projection process, squeezed light, or special interactions among the atoms are not required in this method, it can be widely applied to many systems. The attainable range of the squeezing parameter is S^{-2/5}, where S is the total spin, which is limited by additional fluctuations imposed by coherent light and the spherical nature of the spin distribution.
We address a scheme to enhance the quantum correlations in cavity opto-magnomechanical system by using the coherent feedback loop in the presence of magnon squeezing. The proposed coherent feedback-control allows a significant enhancement of the entanglement of three bipartite subsystems, i.e., photon-phonon, photon-magnon and phonon-magnon. We also study the Einstein-Podolsky-Rosen steering and one-way steering in the presence of thermal effects without imposing additional conditions of asymmetric losses or noises in the subsystems. Furthermore, we investigate the sensitiveness of the scheme …
We apply spin-squeezing techniques to identify and quantify highly multi-partite photonic entanglement in polarization-squeezed light. We consider a practical single-mode scenario, and find that Wineland-criterion polarization squeezing implies entanglement of a macroscopic fraction of the total photons. A Glauber-theory computation of the observable N-photon density matrix, with N up to 100, finds that N-partite entanglement is observable despite losses and without post-selection. We estimate that existing detectors could observe $\sim1000$-partite entanglement from a few dB of polarization s…
The Stokes-parameter operators and the associated Poincare sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a ligh…
The Abbe's diffraction limit restricts the resolution of an optical imaging and lithography system. Coherent Rabi oscillation is shown to be able to overcome the diffraction limit in both optical and atom lithography. In previous studies, semiclassical theory is applied where the driving field is treated as a classical light and quantum fluctuation is neglected. Here, we show that the quantum fluctuation may reduce the visibility of the superresolution pattern. However, by squeezing the photon number fluctuation we are able to significantly increase its visibility.
In this paper, ordinary and amplitude-squared squeezing as well as Wigner functions of single-photon-added coherent state after postselected von Neumann measurements are investigated. The analytical results show that the von Neumann type measurement which is characterized by post-selection and weak value can significantly change the squeezing feature of single-photon-added coherent state. It is also found that the postselected measurement can increase the nonclassicality of the original state in strong measurement regimes. It is anticipated that this work could may provide an alternate and eff…
We develop a general framework to describe interferometric coherent feedback loops and prove that, under any such scheme, the steady-state squeezing of a bosonic mode subject to a rotating wave coupling with a white noise environment and to any quadratic Hamiltonian must abide by a noise-dependent bound that reduces to the 3dB limit at zero temperature. Such a finding is contrasted, at fixed dynamical parameters, with the performance of homodyne continuous monitoring of the output modes. The latter allows one to beat coherent feedback and the 3dB limit under certain dynamical conditions, which…
The manuscript investigates the entropy squeezing of a qubit (two-level atom) interacting with the cavity field in the Schrödinger cat states. The effects of the Schrödinger cat states of the field on the squeezing are examined. Our results suggest that entropy squeezing is not sensitive to the superposition features of two coherent states of the Schrödinger cat states. Furthermore, it is found that entropy squeezing occurs as the qubit initially close to its maximally coherent state, and the qubit initially in the maximally coherent state can generate optimal squeezing. This also demonstrates…
In analogy with the spin-squeezing inequality of Wang and Sanders [Physical Review A 68, 012101 (2003)], we find inequalities describing macroscopic polarization correlations that are obeyed by all classical fields, and whose violation implies entanglement of the photons that make up the optical beam. We consider a realistic and exactly-solvable experimental scenario employing polarization- squeezed light from an optical parametric oscillator (OPO) and find that any two photons separated by less than the OPO coherence time are polarization entangled. The polarization entanglement is robust aga…
The traversal of an elliptically polarized optical field through a thermal vapour cell can give rise to a rotation of its polarization axis. This process, known as polarization self-rotation (PSR), has been suggested as a mechanism for producing squeezed light at atomic transition wavelengths. In this paper, we show results of the characterization of PSR in isotopically enhanced Rubidium-87 cells, performed in two independent laboratories. We observed that, contrary to earlier work, the presence of atomic noise in the thermal vapour overwhelms the observation of squeezing. We present a theory …
We investigate the presence of spin- and planar- squeezing in generalized superpositions of atomic (or spin) coherent states (ACS). Spin-squeezing has been shown to be a useful tool in determining the presence of entanglement in multipartite systems, such as collections of two-level atoms, as well as being an indication of reduced projection noise and sub-shot-noise limited phase uncertainty in Ramsey spectroscopy, suitable for measuring phases $ϕ\sim 0$. On the other hand, planar-squeezed states display reduced projection noise in two directions simultaneously and have been shown to lead to e…
We present the observation of optical fields carrying squeezed vacuum states at sideband frequencies from 10Hz to above 35MHz. The field was generated with type-I optical parametric oscillation below threshold at 1064nm. A coherent, unbalanced classical modulation field at 40MHz enabled the generation of error signals for stable phase control of the squeezed vacuum field with respect to a strong local oscillator. Broadband squeezing of approximately -4dB was measured with balanced homodyne detection. The spectrum of the squeezed field allows a quantum noise reduction of ground-based gravitatio…
We propose and demonstrate a coherent control scheme for stable phase locking of squeezed vacuum fields. We focus on sideband fields at frequencies from 10Hz to 10kHz which is a frequency regime of particular interest in gravitational wave detection and for which conventional control schemes have failed so far. A vacuum field with broadband squeezing covering this entire band was produced using optical parametric oscillation and characterized with balanced homodyne detection. The system was stably controlled over long periods utilizing two coherent but frequency shifted control fields. In orde…
We report the experimental demonstration of directly produced polarization squeezing at 1064 nm from a type I optical parametric amplifier (OPA) based on a periodically poled KTP crystal (PPKTP). The orthogonal polarization modes of the polarization squeezed state are both defined by the OPA cavity mode, and the birefringence induced by the PPKTP crystal is compensated for by a second, but inactive, PPKTP crystal. Stokes parameter squeezing of 3.6 dB and anti squeezing of 9.4 dB is observed.
We investigate the squeezed regions in the phase plane for non-dissipative dynamical systems controlled by SU(1,1) Lie algebra. We analyze such study for the two SU(1,1) generalized coherent states, namely, the Perelomov coherent state (PCS) and the Barut-Girardello Coherent state (BGCS).
We present a scheme for the charging of a quantum battery based on the dynamics of an open quantum system undergoing coherent quantum squeezing and affected by an incoherent squeezed thermal bath. We show that quantum coherence, as instigated by the application of coherent squeezing, are key in the determination of the performance of the charging process, which is efficiency-enhanced at low environmental temperature and under a strong squeezed driving.
Advances in the emerging field of coherent quantum feedback control (CQFC) have led to the development of new capabilities in the areas of quantum control and quantum engineering, with a particular impact on the theory and applications of quantum optical networks. We consider a CQFC network consisting of two coupled optical parametric oscillators (OPOs) and study the squeezing spectrum of its output field. The performance of this network as a squeezed-light source with desired spectral characteristics is optimized by searching over the space of model parameters with experimentally motivated bo…
A monochromatic double-mode coherent light endowed with orthogonally polarized photons propagating collinearly is studied in Degenerate Parametric Amplification. Generation of Hidden Optical- Polarized States is shown by non-zero values of Index of Hidden Optical-Polarization. Squeezing in HOPS is demonstrated by recognizing a Squeezing function. The Non-Classical feature of HOPS is observed by 'degree of Hidden Optical-Polarization' which attains non-classical value 'greater than unity'. The dynamical nature of Generation, Squeezing and Non-Classicality are numerically presented.
We consider an optomechanical cavity with a movable end-mirror as a quantum mechanical oscillator (MO) containing an interacting cigar-shaped Bose-Eisenstein condensate (BEC). It is assumed that both the MO and the BEC interact with the radiation pressure of the cavity field in the red-detuned and weak coupling regimes while the two-body atomic collisions frequency of the BEC and the mechanical spring coefficient of the MO are coherently modulated. By analyzing the scattering matrix we find that a frequency-dependent squeezing is induced to the three subsystems only due to the coherent modulat…
We report new experiments on polarization squeezing using ultrashort photonic pulses in a single pass of a birefringent fiber. We measure what is to our knowledge a record squeezing of -6.8 +/- 0.3 dB in optical fibers which when corrected for linear losses is -10.4 +/- 0.8 dB. The measured polarization squeezing as a function of optical pulse energy, which spans a wide range from 3.5-178.8 pJ, shows a very good agreement with the quantum simulations and for the first time we see the experimental proof that Raman effects limit and reduce squeezing at high pulse energy.
We have studied relative-intensity fluctuations for a variable set of orthogonal elliptic polarization components of a linearly polarized laser beam traversing a resonant $^{87}$Rb vapor cell. Significant polarization squeezing at the threshold level (-3dB) required for the implementation of several continuous variables quantum protocols was observed. The extreme simplicity of the setup, based on standard polarization components, makes it particularly convenient for quantum information applications.
The notion of spin squeezing has been discussed in this paper using the density matrix formalism. Extending the definition of squeezing for pure states given by Kitagawa and Ueda in an appropriate manner and employing the spherical tensor representation, we show that mixed spin states which are non-oriented and possess vector polarization indeed exhibit squeezing. We construct a mixed state of a spin 1 system using two spin 1/2 states and study its squeezing behaviour as a function of the individual polarizations of the two spinors.
Squeezed light is one of the resources of photonic quantum technology. Among the various nonlinear interactions capable of generating squeezing, the optical Kerr effect is particularly easy-to-use. A popular venue is to generate polarization squeezing, which is a special self-referencing variant of two-mode squeezing. To date, polarization squeezing generation setups have been very sensitive to fluctuations of external factors and have required careful tuning. In this work, we report on a development of a new all-fibre setup for polarization squeezing generation. The setup consists of passive …
The coherent population trapping (CPT) effect is used for making compact atomic clocks. There are two types of CPT clocks: the one in which the Raman beams are applied continuously and the one in which two CPT pulses separated by a dark period are applied (Ramsey scheme). It is obvious that the technique of spin squeezing can only be applied to the Ramsey CPT clock to enhance the sensitivity. However, it is not apparent how to adapt to the CPT clock the protocols for the microwave clock using one-axis-twist squeezing (OATS), since the Ramsey CPT clock is not trivially equivalent to the Ramsey …
