Correlation Spectroscopy with Multiqubit-Enhanced Phase Estimation
Helene Hainzer, Dominik Kiesenhofer, Tuomas Ollikainen, Matthias Bock, Florian Kranzl, Manoj K. Joshi, G. Yoeli, R. Blatt, Tuvia Gefen, Christian F. Roos
Ramsey interferometry is a widely used tool for precisely measuring transition frequencies between two energy levels of a quantum system, with applications in time keeping, precision spectroscopy, quantum optics, and quantum information. Often, the coherence time of the quantum system surpasses the one of the oscillator probing the system, thereby limiting the interrogation time and associated spectral resolution. Correlation spectroscopy overcomes this limitation by probing two quantum systems with the same noisy oscillator for a measurement of their transition frequency difference; this technique has enabled very precise comparisons of atomic clocks. Here, we extend correlation spectroscopy to the case of multiple quantum systems undergoing strong correlated dephasing. We model Ramsey correlation spectroscopy with N particles as a multiparameter phase estimation problem and demonstrate that multiparticle correlations can assist in reducing the measurement uncertainties even in the absence of entanglement. We derive precision limits and optimal sensing techniques for this problem and compare the performance of probe states and measurement with and without entanglement. Using one- and two-dimensional ion Coulomb crystals with up to 91 qubits, we experimentally demonstrate the advantage of measuring multiparticle correlations for reducing phase uncertainties and apply correlation spectroscopy to measure ion-ion distances, transition frequency shifts, laser-ion detunings, and path-length fluctuations. Our method can be straightforwardly implemented in experimental setups with globally coherent qubit control and qubit-resolved single-shot readout and is, thus, applicable to other physical systems such as neutral atoms in tweezer arrays. Published by the American Physical Society 2024
Ramsey interferometry is a widely used tool for precisely measuring transition frequencies between two energy levels of a quantum system, with applications in time keeping, precision spectroscopy, quantum optics, and quantum information. Often, the coherence time of the quantum system surpasses the one of the oscillator probing the system, thereby limiting the interrogation time and associated spectral resolution. Correlation spectroscopy overcomes this limitation by probing two quantum systems with the same noisy oscillator for a measurement of their transition frequency difference; this technique has enabled very precise comparisons of atomic clocks. Here, we extend correlation spectroscopy to the case of multiple quantum systems undergoing strong correlated dephasing. We model Ramsey correlation spectroscopy with N particles as a multiparameter phase estimation problem and demonstrate that multiparticle correlations can assist in reducing the measurement uncertainties even in the absence of entanglement. We derive precision limits and optimal sensing techniques for this problem and compare the performance of probe states and measurement with and without entanglement. Using one- and two-dimensional ion Coulomb crystals with up to 91 qubits, we experimentally demonstrate the advantage of measuring multiparticle correlations for reducing phase uncertainties and apply correlation spectroscopy to measure ion-ion distances, transition frequency shifts, laser-ion detunings, and path-length fluctuations. Our method can be straightforwardly implemented in experimental setups with globally coherent qubit control and qubit-resolved single-shot readout and is, thus, applicable to other physical systems such as neutral atoms in tweezer arrays. Published by the American Physical Society 2024
Quantum entanglement, a hallmark of quantum mechanics, offers unprecedented opportunities to revolutionize spectroscopic techniques. This paper explores the theoretical underpinnings and experimental prospects of quantum entanglement-enhanced spectroscopy for the precise probing of coherent dynamics in complex chemical systems. Traditional spectroscopic methods often face limitations in resolution, sensitivity, and the ability to distinguish subtle quantum phenomena due to their reliance on classical light sources. By harnessing entangled photons, it is possible to overcome these limitations, enabling sub-shot-noise measurements, enhanced spectral resolution beyond the diffraction limit, and access to non-classical correlations within molecular systems. We delve into how entangled light can be generated and engineered to interact with molecular ensembles, facilitating the study of processes such as exciton transport, charge transfer, and vibrational energy redistribution with extraordinary fidelity. The methodology section outlines conceptual experimental setups, including entangled two-photon absorption spectroscopy and quantum Ramsey interferometry, discussing the benefits of these approaches over their classical counterparts. We present hypothetical results demonstrating how entanglement can resolve overlapping spectral features, extend coherence lifetimes, and provide unique insights into the quantum pathways governing chemical reactions. The discussion addresses the challenges associated with maintaining entanglement in noisy chemical environments and outlines strategies for mitigating decoherence. Ultimately, entanglement-enhanced spectroscopy represents a transformative paradigm for chemical physics, promising a deeper understanding of fundamental quantum processes that dictate reactivity and function in biological and material sciences.
The use of entanglement in sensing is often motivated by improved sensitivity arising from non-classical correlations among probes. For static signals, however, this quantum advantage in Ramsey spectroscopy with N probes is known to be highly susceptible to dephasing, which severely limits the possible gain from entanglement. In contrast, we consider sensing of signals that vary in time. Considering the simplest example of dephasing by classical white noise, we show that entanglement allows a large increase in bandwidth when estimating the frequency components of a time-dependent signal. Without sacrificing any sensitivity, entanglement allows for an increase in bandwidth by a factor of N. Alternatively, when interrogation times are limited by the signal bandwidth rather than by dephasing, the average estimation uncertainty over a fixed bandwidth is reduced by a factor of N compared with separable states.
I will present our development of global-phase spectroscopy, a Rabi-like metrological protocol inspired by geometric control techniques originally introduced for holonomic quantum gates and based on detuning-dependent Aharonov–Anandan phase. Applied to an optical clock transition, we deployed this method to realize quantum-amplified, time-reversal spectroscopy, yielding 2.4(7) dB metrological gain and 4.0(8) dB laser-noise suppression beyond the standard quantum limit. I will focus on the key metrological advantages of global-phase spectroscopy: i) an intrinsically favorable scaling of sensitivity to local-oscillator high-frequency noise (compared to for Rabi and for Ramsey), and, unlike standard Rabi spectroscopy, ii) featuring quantum enhancement when operated with entangled collective states, such as spin-squeezed inputs. I will close by connecting these results to the broader QIS-NP landscape, highlighting opportunities for applying this protocol to (other) nuclear-spin qubits, nuclear clocks, and other emerging quantum-enhanced sensing and quantum-information platforms.
Ramsey interferometry estimates a detuning from the phase accumulated between two interaction zones, with a resolution set by the interrogation time τ. We propose a single-qudit extension based on Wigner-Majorana (WM) spin-j dynamics, whose internal levels form a multipath interferometer. The enhancement is not generic: ideal QFTD and XD sequences do not densify the central fringe under the population readouts considered. Instead, in manifolds that realize the WM coupling, it arises from coherences between separated ladder states created and recombined by a single near-resonant drive per Ramsey zone. For the qutrit, preparing the central state of a spin-1 WM manifold and measuring its return probability gives P3(Δ)=cos2(Δτ), versus the qubit P2(Δ)=cos2(Δτ/2). The central fringe is thus compressed twofold at fixed τ and the maximal slope doubled in the ideal limit, with contrast ideally unity. For higher-dimensional WM manifolds (odd and even D) the central response sharpens with dimension, but the signal spreads over several channels; we introduce a scalar readout from nearest-neighbor shoulder populations and quantify the resolution-contrast trade-off via the slope SD and contrast CD. We also study robustness to diagonal phase noise from probe-shift fluctuations: under projector-type common-mode dephasing, the WM readouts are less contrast-sensitive than the qubit readout. The robustness is symmetry-selective, not universal: for linear Zeeman dephasing (L=Jz), the large m-separation that compresses the fringe also enhances dephasing, so higher-dimensional readouts become more sensitive, not protected. The WM qutrit is thus a practical operating point for enhanced Ramsey spectroscopy at fixed τ; higher qudits trade extra slope for reduced contrast.
The stability of an optical atomic clock is a critical figure of merit for almost all clock applications. To this end, much optical atomic clock research has focused on reducing clock instability by increasing the atom number, lengthening the coherent interrogation times, and introducing entanglement to push beyond the standard quantum limit. In this work, we experimentally demonstrate an alternative approach to reducing clock instability using a phase estimation approach based on individually controlled atomic ensembles in a strontium (Sr) optical lattice clock. We first demonstrate joint Ramsey interrogation of two spatially resolved atom ensembles that are out of phase with respect to each other, which we call “quadrature Ramsey spectroscopy,” resulting in a factor of 1.36(5) reduction in absolute clock instability as measured with interleaved self-comparisons. We then leverage the rich hyperfine structure of Sr87 to realize independent coherent control over multiple ensembles with only global laser addressing. Finally, we utilize this independent control over four atom ensembles to implement a form of phase estimation, achieving a factor of greater than 3 enhancement in coherent interrogation time and a factor of 2.08(6) reduction in instability over an otherwise identical single-ensemble clock with the same local oscillator and the same number of atoms. We expect that multiensemble protocols similar to those demonstrated here will result in reduction in the instability of any optical lattice clock with an interrogation time limited by the local oscillator. Published by the American Physical Society 2024
Quantum entanglement is a powerful quantum resource for enhancing measurement precision beyond classical limit. % Here we propose an entanglement-enhanced symmetry-protected destructive many-body Ramsey interferometry for precise parameter estimation. % Through matching the symmetry of input states and Hamiltonian, the spectral shift of Ramsey spectroscopy caused by interparticle interaction, noise, decoherence and experimental imperfection can be mitigated for both time-independent and time-dependent signals, as explored in the companion Letter [S. Chen, et al., Ramsey Spectroscopy via Symmetry-Protected Destructive Many-Body Interferometry (submitted)]. % In this work, we show that symmetric entangled input states can further improve the measurement precision of symmetry-protected Ramsey spectroscopy without affecting the measurement accuracy. % Through inputting spin cat states and applying suitable interaction-based readout operations, the measurement precisions of time-independent and time-dependent signals can both approach the Heisenberg limit. % In particular, we systematically analyze how precision scaling and robustness depend on the input states, parameters, experimental imperfection and decoherence. % This work establishes a practical pathway to Heisenberg-limited quantum metrology with many-body Ramsey interferometry, offering resilience against realistic noise and imperfections.