We describe a comagnetometer employing the f=1 and f=2 ground state hyperfine manifolds of a ^{87}Rb spinor Bose-Einstein condensate as colocated magnetometers. The hyperfine manifolds feature nearly opposite gyromagnetic ratios and thus the sum of their precession angles is only weakly coupled to external magnetic fields, while being highly sensitive to any effect that rotates both manifolds in the same way. The f=1 and f=2 transverse magnetizations and azimuth angles are independently measured by nondestructive Faraday rotation probing, and we demonstrate a 44.0(8) dB common-mode rejection in good agreement with theory. We show how the magnetometer coherence time can be extended to ∼1 s, by using spin-dependent interactions to inhibit hyperfine relaxing collisions between f=2 atoms. The technique could be used in high sensitivity searches for new physics on submillimeter length scales, precision studies of ultracold collision physics, and angle-resolved studies of quantum spin dynamics.
We describe a comagnetometer employing the f=1 and f=2 ground state hyperfine manifolds of a ^{87}Rb spinor Bose-Einstein condensate as colocated magnetometers. The hyperfine manifolds feature nearly opposite gyromagnetic ratios and thus the sum of their precession angles is only weakly coupled to external magnetic fields, while being highly sensitive to any effect that rotates both manifolds in the same way. The f=1 and f=2 transverse magnetizations and azimuth angles are independently measured by nondestructive Faraday rotation probing, and we demonstrate a 44.0(8) dB common-mode rejection in good agreement with theory. We show how the magnetometer coherence time can be extended to ∼1 s, by using spin-dependent interactions to inhibit hyperfine relaxing collisions between f=2 atoms. The technique could be used in high sensitivity searches for new physics on submillimeter length scales, precision studies of ultracold collision physics, and angle-resolved studies of quantum spin dynamics.
In this work we demonstrate the first realization of a comagnetormeter in the ultracold regime. In comparison to regular magnetometers, which are designed to maximize their magnetic field sensitivity, a comagnetometer uses paired magnetometers in a differential configuration to cancel the effects of the magnetic field and resolve weak dynamics that differently affect its constituents. Here, we implement a omagnetometer within the f=1 and f=2 ground state hyperfine manifolds of a Rb87 spinor Bose-Einstein condensate (SBEC). The hyperfine manifolds feature nearly opposite gyromagnetic ratios and thus the sum of their precession angles is only weakly coupled to external magnetic fields, while being highly sensitive to any effect that rotates both manifolds in the same way. A fundamental limitation of the comagnetometer is f=2--> f=1 hyperfine relaxing collisions, where the liberated kinetic energy expels colliding atoms from the optical trap. These collisions are state-dependent and can be avoided by preserving the f=2 spin state in a stretched configuration. We show how this can be achieved at low magnetic fields, where the spin-dependent contact interaction is the dominant energy contribution and stabilizes the spin orientation of the SBEC. Under these conditions, the comagnetometer coherence time can be extended to ~1 s and the observed common magnetic field suppression is 44.0(8)dB. The technique is applied to precision measurement of the interhyperfine interaction in 87Rb. The uncertainty in the obtained interhyperfine scattering lengths is reduced by more than a factor three with respect to previously reported values. We also present preliminary studies on phase-resolved parametric amplification within a SBEC comagnetometer. In this case, the f=2 manifold undergoes parametric amplification, while the f=1 manifold keeps track of the rotating reference frame induced by the applied external magnetic field. We describe technical improvements to the experimental system in two areas: magnetic control and manipulation, and optical trapping and probing. The first group of improvements includes the implementation of radiofrequency (rf) and microwave (mw) driving and the development of a real-time rf source. The second group of improvements includes a pulsed optical trapping technique, a digital implementation of the laser locking scheme, and a hyperfine-selective Faraday probing method. Aquesta tesi demostra el primer comagnetòmetre implementat en un sistema d’àtoms ultrafreds. Els magnetòmetres són altament sensibles a canvis en el camp magnètic. Els comagnetòmetres, en canvi, utilitzen magnetòmetres aparellats diferencialment per a cancel·lar la dependència del camp magnètic extern i discernir camps o interaccions que afecten de forma diferent als seus constituents. En aquest treball, s’implementa un comagnetòmetre mitjançant una superposició coherent dels estats hiperfins f=1 i f=2 d’un condensat spinorial de Bose-Einstein de Rb87. Aquests estats tenen fraccions giromagnètiques gairebé oposades, de manera que la suma dels seus angles de precessió no depèn del camp magnètic però es veu doblement afectada per interaccions que roten els dos estats en la mateixa direcció. Col·lisions de relaxació hiperfina f=2 --> f=1 limiten el temps de coherència del comagnetòmetre. En concret, els àtoms que hi participen són expulsats de la trampa òptica degut a l’energia cinètica alliberada en la col·lisió. Aquest tipus de col·lisió depenen de l’estat de spin i es cancel·len per a estats que maximitzen el spin a f =2. En aquesta tesis demostrem la cancel·lació de col·lisions de relaxació hiperfina a camps magnètics baixos, on la interacció de spin és la contribució energètica dominant i estabilitza l’estat a f = 2. Sota aquestes condicions, el temps de coherència del comagnetòmetre s’estén fins a ~1 s i el soroll de camp magnètic es veu atenuat per 44.0(8) dB. El comagnetòmetre s’ha usat per caracteritzar la interacció hiperfina en àtoms de Rb87. En comparació a estudis experimentals anteriors, s’ha aconseguit reduir en un factor tres la incertesa en les longituds de dispersió entre estats hiperfins. També presentem experiments preliminars d’amplificació paramètrica amb resolució de phase, on l’amplificació paramètrica té lloc a f=2 i les rotacions magnètiques del sistema de referència són mesurades de forma simultània a f=1. Els avenços tècnics es divideixen en millores del control i de la manipulació magnètica, així com en millores del confinament i de la detecció òptica. Els primers inclouen els sistemes de manipulació atòmica mitjançant radiofreqüència i microones, com també el desenvolupament d’una font de radiofreqüència amb control en temps real. Els segons inclouen una tècnica de confinament polsat, la digitalització del sistema d’estabilització làser i la detecció òptica d’ambdós estats hiperfins.
Spinor Bose-Einstein condensates (BECs) are multi-component superfluids with magnetic interactions, formed from dilute gases of atoms in the Zeeman sublevels mF of a single hyperfine ground state F. Spinor BECs are inherently magnetic quantum objects, and exhibit a multitude of features such as spin domains, magnon excitations, and distinct magnetic phases. At the heart of the magnetic nature of a spinor BEC is the spin-dependent collisional interaction c, which determines the overall magnetic behaviour of the superfluid. In conjunction with the quadratic Zeeman shift q, the magnitude and sign of c give rise to an intricate magnetic phase diagram. The magnetic phase of a spinor BEC is tunable, and c and q are the knobs. In addition to realising quantum simulators of magnetism, spinor BECs are also precise magnetic sensors. Atomic magnetometry measures the Larmor precession frequency of atoms, which is proportional to the magnetic field strength. The sensitivity of an atomic magnetometer is principally dependent on the duration of the measurement (interrogation time) and number of atoms participating in the measurement. BECs are highly suitable as atomic magnetometers, allowing for long interrogation times and high atomic density, with microscopic sensor volumes. The latter is an important consideration, as measurement of small magnetic sources demand equally microscopic sensors. Established forms of magnetometry (such as warm vapour magnetometers) use large sensing volumes and are not trivially miniaturised. The exquisite sensitivity of a spinor BEC to magnetic fields becomes a liability when one studies low energy (~ 1 Hz) spinor physics over long evolution times (100 ms) in a typical laboratory environment. To first order, the spin-collisional interaction is independent of the magnetic field. However, spatially inhomogeneous magnetic fields are problematic, exerting mechanical forces on the magnetically sensitive spin components, suppressing spin collisions and possibly introducing relaxation mechanisms that confound the observation of intrinsic equilibration. Precise characterisation of magnetic field gradients and their cancellation is thus of paramount importance. In this thesis, the interaction of a spinor BEC with its environment is studied. The construction, operation and optimisation of a BEC machine is described in detail, as well as the quantum state preparation and control techniques used. Spin-mixing collisions were studied by observing population oscillations, the characteristic hallmark of such coherent phenomena. The observed population dynamics showed strong evidence of the deleterious effects of magnetic field gradients. A series of experiments were performed using spin-echo pulse sequences to decouple the evolving spinor condensate from the inhomogeneous magnetic environment with encouraging results, but which posed further questions. The fidelity of spin-echo pulses in the strong radiative coupling regime was also studied. Spinor condensates were then employed as sensitive magnetometers to characterise the magnetic landscape they inhabit. A new method of measuring magnetic field gradients was developed, using a pair of spinor BECs separated in space that are simultaneously addressed by a Ramsey interferometry sequence. Combined with a re-orientable magnetic bias field, the resulting gradiometer was used to measure the magnetic field gradient tensor in vacuo. This scheme can be extended to realise a high-precision vector co-magnetometer, with spatiotemporal sensitivity comparable to established forms of magnetometry. Vector light shifts (VLSs) are optically-induced energy shifts that result in effective magnetic fields, which in our case originate from the laser beams used to trap the atoms. The VLS vanishes for purely linearly polarised light, which is experimentally difficult to obtain in vacuo. Small elliptical polarisation imperfections originating from birefringent optics and the glass vacuum cell result in a non-zero shift that contaminates magnetometry measurements. The VLS is spatially varying due to the intensity gradient of the trapping light. Due to gravitational sag of the trapping potential, the spatial variation of the VLS is accentuated, resulting in an effective magnetic field gradient that contributes to dephasing and component separation. The simultaneous Ramsey interferometry experiments are then adapted to measure the VLS-induced Zeeman shift and diagnose its elimination. Up to 99.96% of the VLS is eliminated using this method, and extensions to the technique are described.
Light spin-zero bosons with scalar and pseudoscalar couplings mediate a parity- and time-reversal-violating monopole-dipole interaction between unpolarized matter and polarized spins. For proton spins, the interaction has been probed directly only at ranges λ≳ 5 mm; below this range, laboratory limits are inferred from neutron-dominated nuclei through nuclear-spin models. We analyze a direct search with a single-domain 87Rb spinor Bose-Einstein condensate in close proximity to a source mass. The F=1 and F=2 manifolds act as two co-located magnetometers that precess in opposite directions in a magnetic field but in the same direction under the exotic interaction. They thus form a natural comagnetometer, in which the sum of their precession angles suppresses field noise by a measured 44 dB and a weighted sum cancels the field altogether. Taking as a starting point the demonstrated magnetometry [Palacios et al. Proc. Nat. Acad. Sci. \textbf{119}, e2115339119 (2022)] and comagnetometry [Gomez et al. Phys. Ref. Lett. \textbf{124}, 170401 (2020)] performance of the 87Rb single-domain spinor condensate at ICFO [Palacios et al. New J. Phys. \textbf{20}, 053008 (2018)], we study the projected sensitivity as a function of source-mass geometry and in-progress improvements to atom loading methods, trap beam geometry, and magnetic environment. With an insulating bismuth germanate source mass with a spherical top, whose apex sits 50 μm below the center of the condensate, one week of acquisition would reach ∣gsNgpp∣≈2×10−22 with these upgrades and 3×10−24 at the projection-noise limit (λ=100μm, 95\% C.L.). This is more than three and five orders of magnitude below existing laboratory limits. The improvement covers boson masses of 0.3-50 meV/c2 after the upgrades and 0.09-70 meV/c2 at the projection-noise limit.
We propose a novel type of composite light–matter magnetometer based on a transversely driven multi-component Bose–Einstein condensate coupled to two distinct electromagnetic modes of a linear cavity. Above the critical pump strength, the change of the population imbalance of the condensate caused by an external magnetic field entails the change of relative photon number of the two cavity modes. Monitoring the cavity output fields thus allows for nondestructive measurement of the magnetic field in real time and we show that the sensitivity of the proposed magnetometer exhibits Heisenberg-like scaling with respect to the atom number. For state-of-the-art experimental parameters, we calculate the lower bound on the sensitivity of such a system to be of the order of [See the attached file] for a condensate of 10⁴ atoms with coherence times on the order of several ms.
We demonstrate a precise magnetic microscope based on direct imaging of the Larmor precession of a 87Rb spinor Bose-Einstein condensate. This magnetometer attains a field sensitivity of 8.3pT/Hz1/2 over a measurement area of $120\text{ }\text{ }\ensuremath{\mu}{\mathrm{m}}^{2}$, an improvement over the low-frequency field sensitivity of modern SQUID magnetometers. The achieved phase sensitivity is close to the atom shot-noise limit, estimated as 0.15pT/Hz1/2 for a unity duty cycle measurement, suggesting the possibilities of spatially resolved spin-squeezed magnetometry. This magnetometer marks a significant application of degenerate atomic gases to metrology.
Abstract We propose a novel type of composite light–matter magnetometer based on a transversely driven multi-component Bose–Einstein condensate coupled to two distinct electromagnetic modes of a linear cavity. Above the critical pump strength, the change of the population imbalance of the condensate caused by an external magnetic field entails the change of relative photon number of the two cavity modes. Monitoring the cavity output fields thus allows for nondestructive measurement of the magnetic field in real time and we show that the sensitivity of the proposed magnetometer exhibits Heisenberg-like scaling with respect to the atom number. For state-of-the-art experimental parameters, we calculate the lower bound on the sensitivity of such a system to be of the order of fT ( H z ) − 1 –pT ( H z ) − 1 for a condensate of 104 atoms with coherence times on the order of several ms.