Implementation of the quantum interferometry concept to spin-1 atomic Bose–Einstein condensates is analyzed by employing a polar state evolved in time. In order to identify the best interferometric configurations, the quantum Fisher information (QFI) is maximized. Three optimal configurations are identified, among which one was not reported in the literature yet, although it gives the highest value of the QFI in experimentally achievable short time dynamics. Details of the most optimal configurations are investigated based on the error-propagation formula which includes the interaction-based readout protocol to reduce the destructive effect of detection noise. In order to obtain Heisenberg scaling accessible by present day experimental techniques, an efficient measurement and a method for the inversion of dynamics were developed, as necessary for the protocol’s implementation.
Implementation of the quantum interferometry concept to spin-1 atomic Bose–Einstein condensates is analyzed by employing a polar state evolved in time. In order to identify the best interferometric configurations, the quantum Fisher information (QFI) is maximized. Three optimal configurations are identified, among which one was not reported in the literature yet, although it gives the highest value of the QFI in experimentally achievable short time dynamics. Details of the most optimal configurations are investigated based on the error-propagation formula which includes the interaction-based readout protocol to reduce the destructive effect of detection noise. In order to obtain Heisenberg scaling accessible by present day experimental techniques, an efficient measurement and a method for the inversion of dynamics were developed, as necessary for the protocol’s implementation.
Recent experiments demonstrated the generation of entanglement by quasiadiabatically driving through quantum phase transitions of a ferromagnetic spin-1 Bose-Einstein condensate in the presence of a tunable quadratic Zeeman shift. We analyze, in terms of the Fisher information, the interferometric value of the entanglement accessible by this approach. In addition to the Twin-Fock phase studied experimentally, we unveil a second regime, in the broken axisymmetry phase, which provides Heisenberg scaling of the quantum Fisher information and can be reached on shorter time scales. We identify optimal unitary transformations and an experimentally feasible optimal measurement prescription that maximize the interferometric sensitivity. We further ascertain that the Fisher information is robust with respect to nonadiabaticity and measurement noise. Finally, we show that the quasiadiabatic entanglement preparation schemes admit higher sensitivities than dynamical methods based on fast quenches.
We develop a time-optimal approach to force sensing using a Bose-Einstein condensate in a shaken optical lattice. Optimal control protocols are derived from a Fisher information framework and yield optimal dynamics that spontaneously organize in intereferometer-like structures, where multiple interferences combine to maximize sensitivity. We analyse how measurement precision scales with control time and how the finite momentum dispersion of the condensate changes the optimal dynamics, observing an abrupt change of conformation from single- to double-folded interference structures for robust controls. The protocols are implemented experimentally for cold atoms subjected to inertial and magnetic forces, demonstrating high sensitivity and robustness. Our approach establishes a general route to time-optimal quantum sensing beyond standard interferometric architectures, applcable across all quantum platforms.
Abstract In this work we address the optimization of two important quantum states in terms of interferometric phase sensitivity, given a constraint on the total average number of input photons, N ¯ We use the quantum Fisher information (QFI) as our main tool. We employ both the single- and two-parameter QFI in order to address detection schemes having, and respectively, not having access to an external phase reference. The first quantum state we consider is the coherent plus squeezed vacuum input and find the optimum coherent fraction that maximizes both the single- and two-parameter QFI. We also discuss detection schemes able to perform almost optimally. Finally, we consider the double squeezed vacuum input and determine the squeezed fraction between the inputs that maximizes the QFI. Similar to the previous input state, we also provide detection schemes able to perform optimally.
Entanglement-enhanced atom interferometry has the potential of surpassing the standard quantum limit and eventually reaching the ultimate Heisenberg bound. The experimental progress is, however, hindered by various technical noise sources, including the noise in the detection of the output quantum state. The influence of detection noise can be largely overcome by exploiting echo schemes, where the entanglement-generating interaction is repeated after the interferometer sequence. Here, we propose an echo protocol that uses two-axis countertwisting as the main nonlinear interaction. We demonstrate that the scheme is robust to detection noise and its performance is superior compared to the already demonstrated one-axis twisting echo scheme. In particular, the sensitivity maintains the Heisenberg scaling in the limit of a large particle number. Finally, we show that the protocol can be implemented with spinor Bose-Einstein condensates. Our results thus outline a realistic approach to mitigate the detection noise in quantum-enhanced interferometry.
Interferometry with ultracold atoms promises the possibility of ultraprecise and ultrasensitive measurements in many fields of physics, and is the basis of our most precise atomic clocks. Key to a high sensitivity is the possibility to achieve long measurement times and precise readout. Ultracold atoms can be precisely manipulated at the quantum level and can be held for very long times in traps; they would therefore be an ideal setting for interferometry. In this paper, we discuss how the nonlinearities from atom–atom interactions, on the one hand, allow us to efficiently produce squeezed states for enhanced readout and, on the other hand, result in phase diffusion that limits the phase accumulation time. We find that low-dimensional geometries are favorable, with two-dimensional (2D) settings giving the smallest contribution of phase diffusion caused by atom–atom interactions. Even for time sequences generated by optimal control, the achievable minimal detectable interaction energy Δ E min is of the order of 10 −4 μ, where μ is the chemical potential of the Bose–Einstein condensate (BEC) in the trap. From these we have to conclude that for more precise measurements with atom interferometers, more sophisticated strategies, or turning off the interaction-induced dephasing during the phase accumulation stage, will be necessary.
Quantum Fisher information (QFI) determines the ultimate precision of a quantum sensor after optimization over all allowed measurements, but it does not quantify how difficult the optimal readout is to implement. We introduce a moment Fisher hierarchy FM(k), which measures the fraction of QFI accessible to collective spin moments up to degree k, together with a readout-complexity scale k90 defined by the minimum degree required to recover 90% of the QFI. Applying this framework to a nonlinear collective-spin sensor, we show that many-body dynamics can preserve large QFI while transferring the optimal readout into high-rank SU(2) tensor sectors inaccessible to low-order collective observables. For system sizes up to N=100, first moments access only ∼10−2 of the available QFI, while the degree required to recover 90% of it grows to k90≃28. A rank-resolved analysis of the symmetric logarithmic derivative (SLD) under weak damping shows that the nonlinear protocol pushes the optimal readout toward the highest available tensor ranks while strongly depleting its low-rank weight. These results identify nonlinear tangent-space shear as the mechanism behind a finite-size readout-complexity bottleneck in many-body quantum metrology.