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 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 the help of a tailored excited and entangled many-body state of a noninteracting Bose-Einstein condensate. We identify corresponding optimal measurements and argue that even finite temperature as a source of decoherence is, in principle, rather favorable for the obtainable precision scaling.
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 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 the help of a tailored excited and entangled many-body state of a noninteracting Bose-Einstein condensate. We identify corresponding optimal measurements and argue that even finite temperature as a source of decoherence is, in principle, rather favorable for the obtainable precision scaling.
Multimode squeezing and entanglement are important resources in quantum metrology and sensing. For spin-1/2 Bose-Einstein condensates subject to spin-orbit coupling (SOC), previous studies on spin squeezing have been limited to two-mode systems. In this work, we demonstrate that such a system can naturally construct a four-mode model spanning an su(4) algebra with six SU(2) subspaces. Using spin squeezing parameters and quantum Fisher information matrices, we analyze the dynamical evolution of coherent spin states. The results show that, beyond two-mode models, the SOC-induced four-mode couplings give rise to richer entanglement-enhanced sensing approaching the Heisenberg limit across various SU(2) subspaces. Additionally, by tuning a single system parameter (the Raman Rabi frequency), one can selectively control the optimal measurement across different subspaces.
We propose a spin-motion state for high-precision quantum metrology with super-Heisenberg scaling of the parameter estimation uncertainty using a trapped ion system. Such a highly entangled state can be created using the Tavis-Cummings Hamiltonian which describes the interaction between a collective spin system and a single vibrational mode. Our method relies on an adiabatic evolution in which the initial motional squeezing is adiabatically transferred into collective spin squeezing. In the weak squeezing regime, we show that the adiabatic evolution creates a spin-squeezed state, which reduces the quantum projective noise to a sub-shot noise limit. For strong bosonic squeezing we find that the quantum Fisher information follows a super-Heisenberg scaling law ∝N5/2 in terms of the number of ions N. Furthermore, we discuss the spin squeezing parameter which quantifies the phase sensitivity enhancement in Ramsey spectroscopic measurements and show that it also exhibits a super-Heisenberg scaling with N. Our work enables the development of high-precision quantum metrology based on entangled spin-boson states that lead to faster scaling of the parameter estimation uncertainty with the number of spins.
We propose a method to perform precision measurements of the interaction parameters in systems of N ultracold spin 1∕2 atoms. The spectroscopy is realized by first creating a coherent spin superposition of the two relevant internal states of each atom and then letting the atoms evolve under a squeezing Hamiltonian. The nonlinear nature of the Hamiltonian decreases the fundamental limit imposed by the Heisenberg uncertainty principle to ${N}^{\ensuremath{-}2}$, a factor of N smaller than the fundamental limit achievable with noninteracting atoms. We study the effect of decoherence and show that, even with decoherence, entangled states can outperform the signal to noise limit of nonentangled states. We present two possible experimental implementations of the method using Bose-Einstein spinor condensates and fermionic atoms loaded in optical lattices and discuss their advantages and disadvantages.
Quantum Sensors, like atom interferometers (AI), can be employed for high-precision measurements of inertial forces, including their application as gravimeters, gradiometers, accelerometers, and gyroscopes. Their measurement principle relies on ultracold atoms that are prepared in quantum-mechanical superposition states in external degrees of freedom. These states can be prepared by a momentum transfer of a Raman laser. Then the superposition state senses the effect of an inertial force, which induce a corresponding relative phase. The phase is read out by a final coupling which converts the interferometric phase into a atom number difference between the two states. The difference provides an estimate of the interferometric phase and the corresponding quantity of interest. The quantum mechanical noise of the atomic ensemble cause a fundamental uncertainty of this estimation, which I analyze for generic AIs. For small atomic densities, the quantum phase noise of the ensemble limits the interferometric sensitivity. For large densities, quantum number fluctuations generate density fluctuations, which generates phase noise. I show that these two competing effects result in an optimal atom number with a maximal interferometer resolution. Squeezed atomic samples allow for a reduction of the quantum noise of one quantity at the expense of an increased noise along of a conjugate quantity. Phase and number are such quantities which obey to a variant of Heisenberg’s uncertainty principle. Neither phase nor number squeezing can improve the maximal interferometer resolution. As one main result of this thesis, I show how an optimal squeezing in between number and phase squeezing, allows for a fundamental improvement. I evaluate possible experimental paths to implement the proposed protocol. Concepts for a squeezing-enhanced operation of external-degree AIs have not yet been demonstrated. I propose and implement an atomic gravimeter, which is designed to accept spin-squeezed atomic states as input states. The interferometer is designed such that the interferometer couplings are performed in spin space, while the phase accumulation is performed in momentum states. For this interferometer, the squeezed input can be directly obtained from spin dynamics in spinor Bose-Einstein condensates. The main noise contributions in the experiment are analyzed, which results in a factor of 84 above the relevant quantum limit, preventing a squeezing enhancement so far. I outline a suppression of the main noise source, uncontrolled AC Stark shift on the squeezed mode and propose future important applications, including test of spontaneous collapse theories and an improvement of large-scale, high-precision gradiometers.
Bosonic systems, such as photons and ultracold atoms, have played a central role in demonstrating quantum-enhanced sensing. Quantum entanglement, through squeezed and GHZ states, enables sensing beyond classical limits. However, such a quantum advantage has so far been confined to two-mode bosonic systems, as analogous multi-mode squeezed states are non-trivial to prepare. Here, we develop a Monte-Carlo based optimization technique which can be used to efficiently engineer a Hamiltonian control-sequence for multi-mode bosonic systems to prepare multi-mode squeezed states. Specifically, we consider a Bose-Einstein condensate in an optical lattice, relevant for applications in gravimetry and gradiometry, and demonstrate that metrologically useful squeezed states can be generated using the Bose-Hubbard Hamiltonian which includes on-site atomic interactions, tunable via Feshbach resonances. By analyzing the distribution (density) of the quantum Fisher information (QFI) over the Hilbert space, we identify a characteristic \textit{intermediate scaling} of the QFI: O(N2L+L2N), which lies between the standard quantum limit (SQL) and the Heisenberg limit (HL) for N atoms in L modes. We show that in general, within the Hilbert space there is a finite, O(1) measure subset of Hilbert space with an intermediate QFI scaling. Therefore, one can find a Hamiltonian control sequence using a Monte Carlo optimization over random control sequences, that produces a state with intermediate scaling of the QFI. We assume an experimentally accessible range of the control parameters in the Hamiltonian resources and show that the intermediate scaling can be readily achieved. Our results indicate that the HL can be approached in quantum gravimetry using realistic experimental parameters for systems with L=O(1) and N≫L.
We observe spin squeezing in three-component Bose gases where all three hyperfine states are coupled by synthetic spin-orbit coupling. This phenomenon is a direct consequence of spin-orbit coupling, as can be seen clearly from an effective spin Hamiltonian. By solving this effective model analytically with the aid of a Holstein-Primakoff transformation for a spin-1 system in the low excitation limit, we conclude that the spin-nematic squeezing, a category of spin squeezing existing exclusively in large spin systems, is enhanced with increasing spin-orbit coupling intensity and effective Zeeman field, which correspond to Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{R}$ and two-photon detuning $\ensuremath{\delta}$ within the Raman scheme for synthetic spin-orbit coupling, respectively. These trends of dependence are in clear contrast to spin-orbit-coupling-induced spin squeezing in spin-1/2 systems. We also analyze the effects of harmonic trap and interparticle interaction with realistic experimental parameters numerically, and find that a strong harmonic trap favors spin-nematic squeezing. We further show spin-nematic squeezing can be interpreted as two-mode entanglement or two-spin squeezing at low excitation. Our findings can be observed in 87Rb gases with existing techniques of synthetic spin-orbit coupling and spin-selective imaging.