Spin-spin interactions generated by a detuned cavity are a standard mechanism for generating highly entangled spin squeezed states. We show here how introducing a weak detuned parametric (two-photon) drive on the cavity provides a powerful means for controlling the form of the induced interactions. Without a drive, the induced interactions cannot generate Heisenberg-limited spin squeezing, but a weak optimized drive gives rise to an ideal two-axis twist interaction and Heisenberg-limited squeezing. Parametric driving is also advantageous in regimes limited by dissipation, and enables an alternate adiabatic scheme which can prepare optimally squeezed, Dicke-like states. Our scheme is compatible with a number of platforms, including solid-state systems where spin ensembles are coupled to superconducting quantum circuits or mechanical modes.
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 analyze a model for spin squeezing based on the so-called counter-twisting Hamiltonian, including the effects of dissipation and finite system size. We discuss the conditions under which the Heisenberg limit, i.e. phase sensitivity $\propto 1/N$, can be achieved. A specific implementation of this model based on atom-atom interactions via quantized photon exchange is presented in detail. The resulting excitation corresponds to the creation of spin-flipped atomic pairs and can be used for fast generation of entangled atomic ensembles, spin squeezing and apllications in quantum information pro…
We systematically study the influence of amplitude modulation on the steady-state bosonic squeezing and entanglement in a dissipative three-mode optomechanical system, where a vibrational mode of the membrane is coupled to the left and right cavity modes via the radiation pressure. Numerical simulation results show that the steady-state bosonic squeezing and entanglement can be significantly enhanced by periodically modulated external laser driving either or both ends of the cavity. Remarkably, the fact that as long as one periodically modulated external laser driving either end of the cavitie…
Two well-known mechanisms, one-axis twisting (OAT) and two-axis countertwisting (TACT), generate spinsqueezed states dynamically. The latter provides better spin squeezing (SS) but has not been demonstrated as the form of its interaction does not occur naturally in known physical systems. Several proposals for realizing effective TACT transformed from OAT require stringent experimental conditions in order to overcome the resulting nonstationary (oscillating) SS and continuously varying mean spin directions. This work presents a simple scheme that solves both problems by freezing SS at an optim…
We reconsider the one-axis twisting Hamiltonian, which is commonly used for generating spin squeezing, and treat its dynamics within the Heisenberg operator approach. To this end we solve the underlying Heisenberg equations of motion perturbatively and evaluate the expectation values of the resulting time-dependent Heisenberg operators in order to determine approximately the dynamics of spin squeezing. Comparing our results with those originating from exact numerics reveals that they are more accurate than the commonly used frozen spin approximation.
We present a generalized echo squeezing protocol (GESP) as a generalization of the Schrödinger cat state protocol (SCSP) with the value of the squeezing parameter being an arbitrary number rather than pi/2. We show analytically that over a broad range of the squeezing parameter the sensitivity reaches the Heisenberg limit (HL) within a factor of root-2. For a large number of particles, N, this plateau interval is almost the whole range from zero to pi/2, and the sensitivity is independent of the parity of N. Therefore, it is possible to operate a sensor over a wide interval of the squeezing pa…
We study the effect of the intermode coupling in the generation of coherence when two bosonic modes are bilinearly coupled. We consider the case for which the two modes are weakly coupled and the rotating-wave approximation (RWA) applies and the case for which they are strongly coupled and the (RWA) does not apply. Then, in the regime of validity of (RWA), there is no coherence generation solely due to squeezing effects, which means there is an exchange of excitation between the modes and negligible squeezing. On the other hand, if the two modes are strongly coupled coherence is generated by t…
Large optical nonlinearities can have numerous applications, ranging from the generation of cat-states for optical quantum computation, through to quantum sensing where the sensitivity exceeds Heisenberg scaling in the resources. However, the generation of ultra-large optical nonlinearities has proved immensely challenging experimentally. We describe a novel protocol where one can effectively generate large optical nonlinearities via the conditional application of a linear operation on an optical mode by an ancilla mode, followed by a measurement of the ancilla and corrective operation on the …
In this paper, we study the quantum properties for a system that consists of a central atom interacting with surrounding spins through the Heisenberg $XX$ couplings of equal strength. Employing the Heisenberg equations of motion we manage to derive an exact solution for the dynamical operators. We consider that the central atom and its surroundings are initially prepared in the excited state and in the coherent spin state, respectively. For this system, we investigate the evolution of variance squeezing and entanglement. The nonclassical effects have been remarked in the behavior of all compon…
We propose to simulate bosonic pair creation using large arrays of long-lived dipoles with multilevel internal structure coupled to an undriven optical cavity. Entanglement between the atoms, generated by the exchange of virtual photons through a common cavity mode, grows exponentially fast and is described by two-mode squeezing of effective bosonic quadratures. The mapping between an effective bosonic model and the natural spin description of the dipoles allows us to realize the analog of optical homodyne measurements via straightforward global rotations and population measurements of the ele…
The work is organized in two main topics. At first we will outline the relation between spin squeezing, quantum metrology and entanglement detection, with a particular focus on the last. We will derive spin squeezing criteria for the detection of entanglement and its depth that outperform past approaches, especially for unpolarized states, recently produced in experiments and object of increasing interest in the community. Furthermore, we will extend the original definition of spin squeezed states by providing a new parameter that is thought to embrace different classes of states in a unified …
We predict that exploiting spin-orbit coupling in a harmonically trapped spinor quantum gas can lead to scaling of the optimal measurement precision beyond the Heisenberg scaling. We show that quadratic scaling with the number of atoms can be facilitated via squeezed center-of-mass excitations of the atomic motion using a 1D spin-orbit coupled fermions or strongly interacting bosons (Tonks-Girardeau gas). Based on predictions derived from analytic calculations of the corresponding quantum Fisher information, we then introduce a protocol which overcomes the Heisenberg scaling (and limit) with h…
We discuss how large amounts of steady-state quantum squeezing (beyond 3 dB) of a mechanical resonator can be obtained by driving an optomechanical cavity with two control lasers with differing amplitudes. The scheme does not rely on any explicit measurement or feedback, nor does it simply involve a modulation of an optical spring constant. Instead, it uses a dissipative mechanism with the driven cavity acting as an engineered reservoir. It can equivalently be viewed as a coherent feedback process, obtained by minimally perturbing the quantum nondemolition measurement of a single mechanical qu…
We consider imperfect two-mode bosonic quantum transducers that cannot completely transfer an initial source-system quantum state due to insufficient coupling strength or other non-idealities. We show that such transducers can generically be made perfect by using interference and phase-sensitive amplification. Our approach is based on the realization that a particular kind of imperfect transducer (one which implements a swapped quantum non-demolition (QND) gate) can be made into a perfect one-way transducer using feed-forward and/or injected squeezing. We show that a generic imperfect transduc…
Equivalent approaches to determine eigenfrequencies of the Liouvillians of open quantum systems are discussed using the solution of the Heisenberg-Langevin equations and the corresponding equations for operator moments. A simple damped two-level atom is analyzed to demonstrate the equivalence of both approaches. The suggested method is used to reveal the structure as well as eigenfrequencies of the dynamics matrices of the corresponding equations of motion and their degeneracies for interacting bosonic modes described by general quadratic Hamiltonians. Quantum Liouvillian exceptional and diabo…
We present results on the digital quantum simulations of beam-splitter and squeezing interactions. The bosonic hamiltonians are mapped to qubits and then digitalized in order to implement them in the IBM quantum devices. We use error mitigation and post-selection to achieve high-fidelity digital quantum simulations of single-mode and two-mode interactions, as evidenced -- where possible -- by full tomography of the resulting states. We achieve fidelities above 90 \% in the case of single-mode squeezing with low squeezing values and ranging from 60 \% to 90 \% for large squeezing and in the mor…
We show how the entangled photons produced in parametric down conversion can be used to improve the sensitivity of a Sagnac interferometer. Two-photon and four-photon coincidences increases the sensitivity by a factor of two and four respectively. Our results apply to sources with arbitrary pumping and squeezing parameters.
We discuss the theory and experimental considerations of a quantum feedback scheme for producing deterministically reproducible spin squeezing. Continuous nondemolition atom number measurement from monitoring a probe field conditionally squeezes the sample. Simultaneous feedback of the measurement results controls the quantum state such that the squeezing becomes unconditional. We find that for very strong cavity coupling and a limited number of atoms, the theoretical squeezing approaches the Heisenberg limit. Strong squeezing will still be produced at weaker coupling and even in free space (t…
We propose schemes for the unconditional preparation of a two-mode squeezed state of effective bosonic modes realized in a pair of atomic ensembles interacting collectively with optical cavity and laser fields. The scheme uses Raman transitions between stable atomic ground states and under ideal conditions produces pure entangled states in the steady state. The scheme works both for ensembles confined within a single cavity and for ensembles confined in separate, cascaded cavities.
We present a new method to compute short-time expectation values in large collective spin systems with generic Markovian decoherence. Our method is based on a Taylor expansion of a formal solution to the equations of motion for Heisenberg operators. This expansion can be truncated at finite order to obtain virtually exact results at short times that are relevant for metrological applications such as spin squeezing. In order to evaluate the expansion for Heisenberg operators, we compute the relevant structure constants of a collective spin operator algebra. We demonstrate the utility of our met…
In two-component BEC, the one-axis twisting Hamiltonian leads to spin squeezing with the limitation that scales with the number of atoms as $N^{-\frac{2}{3}}$. We propose a scheme to transform the one-axis twisting Hamiltonian into a two-axis twisting Hamiltonian, resulting in enhanced spin squeezing $\propto N^{-1}$ approaching the Heisenberg limit. Instead of pulse sequences, only one continuous driving field is required to realizing such transforming, thus the scheme is promising for experiment realizations, to an one-axis twisting Hamiltonian. Quantum information processing and quantum met…
We study the quantum critical effect enhanced spin-nematic squeezing and quantum Fisher information (QFI) in the spin-1 dipolar atomic Bose-Einstein condensate. We show that the quantum phase transitions can improve the squeezing and QFI in the nearby regime of critical point, and the Heisenberg-limited high-precision metrology can be obtained. The different properties of the ground squeezing and entanglement under even and odd number of atoms are further analyzed, by calculating the exact analytical expressions.We also demonstrate the squeezing and entanglement generated by the spin-mixing dy…
We propose a simple method for generating spin squeezing of atomic ensembles in a Floquet cavity subject to a weak, detuned two-photon driving. We demonstrate that {\it the weak squeezing of light inside the cavity can, counterintuitively, induce strong spin squeezing}. This is achieved by exploiting the anti-Stokes scattering process of a photon pair interacting with an atom. Specifically, {\it one photon of the photon pair is scattered into the cavity resonance by absorbing partially the energy of the other photon whose remaining energy excites the atom}. The scattering, combined with a Floq…
These two accompanying papers treat two mode entanglement for systems of identical massive bosons and the relationship to spin squeezing and other quantum correlation effects. Entanglement is a key quantum feature of composite systems where the probabilities for joint measurements on the composite sub-systems are no longer determined from measurement probabilities on the separate sub-systems. We focus on the meaning of entanglement, the quantum paradoxes associated with entangled states, and important tests that allow an experimentalist to determine whether a quantum state - in particular, one…
Two-mode squeezed vacuum states are a crucial component of quantum technologies. In the microwave domain, they can be produced by Josephson ring modulator which acts as a three-wave mixing non-degenerate parametric amplifier. Here, we solve the master equation of three bosonic modes describing the Josephson ring modulator with a novel numerical method to compute squeezing of output fields and gain at low signal power. We show that the third-order interaction from the three-wave mixing process intrinsically limits squeezing and reduces gain. Since our results are related to other general cavity…
Zero-point energy of a trapped ultracold Fermi gas at unitarity: squeezing the Heisenberg uncertainty principle and suppressing the Pauli principle to produce a superfluid state
We present a scheme to generate steady-state atomic spin squeezing in a cavity QED system using cavity-mediated Raman transitions to engineer effective atom-photon interactions, which include both linear and nonlinear (dispersive) atom-cavity couplings, on a potentially equal footing. We focus on a regime where the dispersive coupling is very large and find that the steady state of the system can in fact be a strongly spin-squeezed Dicke state, $|N/2,0\rangle$, of the atomic ensemble. These states offer Heisenberg-limited metrological properties and feature genuine multipartite entanglement am…
Realizing useful quantum operations with high fidelity is a two-task quantum control problem wherein decoherence is to be suppressed and desired unitary evolution is to be executed. The dynamical decoupling (DD) approach to decoherence suppression has been fruitful but synthesizing DD fields with certain quantum control fields may be experimentally demanding. In the context of spin squeezing, here we explore an unforeseen possibility that continuous DD fields may serve dual purposes at once. In particular, it is shown that a rather simple configuration of DD fields can suppress collective deco…
Building robust instruments capable of making interferometric measurements with precision beyond the standard quantum limit remains an important goal in many metrology laboratories. We describe here the basic concepts underlying spin squeezing experiments that allow one to surpass this limit. In priniciple it is possible to reach the so-called Heisenberg limit, which constitutes an improvement in precision by a factor $\sqrt{N}$, where $N$ is the number of particles on which the measurement is carried out. In particular, we focus on recent progress toward implementing spin squeezing with a clo…
Spin squeezed states are a class of entangled states of spins that have practical applications to precision measurements. In recent years spin squeezing with one-axis twisting (OAT) has been demonstrated experimentally with spinor BECs with more than 10^3 atoms. Although the noise is below the standard quantum limit, the OAT scheme cannot reduce the noise down to the ultimate Heisenberg limit. Here we propose an experimentally feasible scheme based on optimized quantum control to greatly enhance the performance of OAT to approach the Heisenberg limit, requiring only an OAT Hamiltonian and the …
