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arXiv:2404.19685 · Physical Review A

Twist-and-turn dynamics of spin squeezing in bosonic Josephson junctions: Enhanced shortcuts-to-adiabaticity approach

Manuel Odelli, A. Ruschhaupt, Vladimir M. Stojanović

Published Aug 12, 2024• 8 citations

Abstract

The twist-and-turn dynamics of spin squeezing results from the interplay of the one-axis-twisting (nonlinear in the collective-spin operators) and the transverse-field turning (linear) term in the underlying Lipkin-Meshkov-Glick-type Hamiltonian, both with constant (time-independent) prefactors. Using shortcuts to adiabaticity (STA) and the recently developed enhanced version thereof (eSTA), we demonstrate here that dynamics of this type can be utilized for a fast and robust preparation of spin-squeezed states in internal bosonic Josephson junctions, i.e., condensates of cold bosonic atoms in two different internal (hyperfine) states (single-boson modes) coupled through Rabi rotations. Assuming that the initial state of this system is its ground state for a given initial value of the (time-dependent) linear coupling strength and that the nonlinear coupling strength remains constant, we set out to determine the time dependence of the linear (Rabi) coupling strength that allows for the generation of spin-squeezed states using the STA- and eSTA-based approaches. We then characterize the modified twist-and-turn dynamics of this system by evaluating the coherent spin-squeezing and number-squeezing parameters, as well as the fidelity of the target spin-squeezed states. In this way, we show that the eSTA approach allows for a particularly robust realization of strongly spin-squeezed states in this system, consistently outperforming its adiabatic and STA-based counterparts, even for systems with several hundred particles. Our method could also be employed for the generation of metrologically-useful non-Gaussian states.

DOI: 10.1103/physreva.110.022610

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We investigate a time-efficient and robust preparation of spin-squeezed states---a class of states of interest for quantum enhanced metrology---in internal bosonic Josephson junctions with a time-dependent nonlinear coupling strength between atoms in two different hyperfine states. We treat this state-preparation problem, which had previously been addressed using shortcuts to adiabaticity (STA), using the recently proposed analytical modification of this class of quantum control protocols that has become known as the enhanced STA (eSTA) method. We characterize the state-preparation process by evaluating the time dependence of the coherent spin-squeezing and number-squeezing parameters and the target-state fidelity. We show that the state-preparation times obtained using the eSTA method compare favorably to those found in previously proposed approaches. We also demonstrate that the increased robustness of the eSTA approach---compared to its STA counterpart---leads to additional advantages for potential experimental realizations of strongly spin-squeezed states in internal bosonic Josephson junctions.

The creation and manipulation of quantum entanglement is central to improving precision measurements. A principal method of generating entanglement for use in atom interferometry is the process of spin squeezing whereupon the states become more sensitive to

\text{SU}(2)

rotations. One possibility to generate this entanglement is provided by one-axis twisting (OAT), where a many-particle entangled state of one degree of freedom is generated by a nonlinear Hamiltonian. We introduce a method which goes beyond OAT to create squeezing and entanglement across two distinct degrees of freedom. We present our work in the specific physical context of a system consisting of collective atomic energy levels and discrete collective momentum states, but also consider other possible realizations. Our system uses a nonlinear Hamiltonian to generate dynamics in

\text{SU}(4)

, thereby creating the opportunity for dynamics not possible in typical

\text{SU}(2)

one-axis twisting. This leads to three axes undergoing twisting due to the two degrees of freedom and their entanglement, with the resulting potential for a more rich context of quantum entanglement. The states prepared in this system are potentially more versatile for use in multiparameter or auxiliary measurement schemes than those prepared by standard spin squeezing.

In this article we consider a bosonic Josephson junction, a model system composed by two coupled nonlinear quantum oscillators which can be implemented in various physical contexts, initially prepared in a product of weakly populated coherent states. We quantify the maximum achievable entanglement between the modes of the junction and then use shortcuts to adiabaticity , a method developed to speed up adiabatic quantum dynamics, as well as numerical optimization, to find time-dependent controls (the nonlinearity and the coupling of the junction) which bring the system to a maximally entangled state.

Spontaneous symmetry breaking is a property of Hamiltonian equilibrium states which, in the thermodynamic limit, retain a finite average value of an order parameter even after a field coupled to it is adiabatically turned off. In the case of quantum spin models with continuous symmetry, we show that this adiabatic process is also accompanied by the suppression of the fluctuations of the symmetry generator-namely, the collective spin component along an axis of symmetry. In systems of S=1/2 spins or qubits, the combination of the suppression of fluctuations along one direction and of the persistence of transverse magnetization leads to spin squeezing-a much sought-after property of quantum states, both for the purpose of entanglement detection as well as for metrological uses. Focusing on the case of XXZ models spontaneously breaking a U(1) [or even SU(2)] symmetry, we show that the adiabatically prepared states have nearly minimal spin uncertainty; that the minimum phase uncertainty that one can achieve with these states scales as N^{-3/4} with the number of spins N; and that this scaling is attained after an adiabatic preparation time scaling linearly with N. Our findings open the door to the adiabatic preparation of strongly spin-squeezed states in a large variety of quantum many-body devices including, e.g., optical-lattice clocks.

Spin squeezing in collective atomic ensembles enables quantum-enhanced metrology by reducing noise below the standard quantum limit through nonlinear interactions. Extending the one-axis and two-axis twisting paradigms of Kitagawa and Ueda, we introduce a general class of three-axis spin squeezed states within the anisotropic Lipkin-Meshkov-Glick model. The model features direction-dependent quadratic couplings that interpolate between uniaxial and biaxial regimes and can be interpreted as an asymmetric quantum rotor. Using semiclassical dynamics, Majorana representations, and Husimi-Q distributions, we analyze the structure and metrological properties of the resulting states. The three-axis framework reproduces the known N^(-2/3) scaling of one-axis twisting and the Heisenberg-limited N^(-1) scaling of two-axis twisting, while allowing additional tunability and enhanced entanglement generation in low-spin systems. We further show that tuning the anisotropy parameters induces ground-state and excited-state quantum phase transitions, including a second-order transition associated with level clustering and critical dynamics. These results unify spin squeezing, quantum criticality, and rotor analogies, and suggest implementations in Rydberg arrays and cavity-QED platforms for precision sensing and quantum simulation.

Spin squeezing is vitally important in quantum metrology and quantum information science. The noise reduction resulting from spin squeezing can surpass the standard quantum limit and even reach the Heisenberg limit (HL) in some special circumstances. However, systems that can reach the HL are very limited. Here, we study the spin squeezing in atomic systems with a generic form of the quadratic collective-spin interaction, which can be described by the Lipkin-Meshkov-Glick model. We find that the squeezing properties are determined by the initial states and the anisotropic parameters. Moreover, we propose a pulse rotation scheme to transform the model into a two-axis twisting model with Heisenberg-limited spin squeezing. Our study paves the way for reaching HL in a broad variety of systems.