Continuously observing a dynamically decoupled spin-1 quantum gas

Abstract

We continuously observe dynamical decoupling in a spin-1 quantum gas using a weak optical measurement of spin precession. Continuous dynamical decoupling aims to dramatically modify the character and energy spectrum of spin states to render them insensitive to parasitic fluctuations. Continuous observation measures this new spectrum in a single-preparation of the quantum gas. The measured time-series contains seven tones, which spectrogram analysis parses as splittings, coherences, and coupling strengths between the decoupled states in real-time. With this we locate a regime where a transition between two states is decoupled from magnetic field instabilities up to fourth order, complementary to the parallel work at higher fields by Trypogeorgos et al. (arXiv:1706.07876). The decoupled microscale quantum gas offers magnetic sensitivity in a tunable band, persistent over many milliseconds: the length scales, frequencies, and durations relevant to many applications, including sensing biomagnetic phenomena such as neural spike trains.From Hahn echoes to dynamical decoupling, pulse sequences have been used to protect spin superpositions from inhomogeneities and parasitic fluctuations, prolonging quantum coherence and circumventing deleterious energy shifts [1][2][3]. A complementary strategy is continuous dynamical decoupling: replacing the pulse sequence with an uninterrupted coupling of bare spin states yielding dressed spin eigenstates with new quantization direction, spectrum, and coupling. The new spectrum protects against low-frequency fluctuations, while the new couplings admit band-tunable sensing [4]. Continuous dynamical decoupling has been applied to nitrogen-vacancy centers [5][6][7][8] Here we demonstrate how a weak continuous measurement of spin precession can probe the spectrum of a continuously decoupled spin-1 quantum gas in a single experimental preparation ('shot'). Time-resolved Fourier spectroscopy of this measurement record reveals not only all dressed-state splittings and their relative immunity to noise but also dressed state coherences and coupling strengths. Estimating the eigenspectrum of the multi-level dressed system brings into view a higherorder decoupling than exists in dynamically-decoupled two-level systems. In this regime, one transition is only quartically-sensitive to noise, surviving much larger amplitude fluctuations than conventional quadratic decoupling. Further, a new transition arises between states which are otherwise uncoupled, completing a cyclic coupling of all dressed states. This low-frequency magnetic stability combined with continuous detection is immediately applicable to band-tunable magnetometry [5,6,12] and experiments preparing delicate spin-entangled manybody states [13]; whereas the unconventional cyclic coupling could be applied to emulation of frustrated quantum spin chains [14].Atomic Zeeman states |m z = −1, 0, 1 in a magnetic field B z e z can be decoupled from fluctuations in B z by applying a perpendicular radiofrequency (rf) field B rf e x cos ω rf t...

Realization of a deeply subwavelength adiabatic optical lattice

“…We first coupled these states with strength rf /2π = 134.5(1) kHz, using a strong radio frequency (rf) magnetic field oscillating along e x with angular frequency ω Z . This made a trio of dressed states [21][22][23] which we denote by |m = −1 , |0 , and |+1 with energieshω ±1,0 . Unlike the bare m F states, every pair of these states can be Raman coupled using lasers detuned far from resonance as compared to the excited-state hyperfine splitting [21].…”

Topological features without a lattice in Rashba spin-orbit coupled atoms

“…An RF magnetic field oscillating at the Larmor frequency with strength Ω RF = 1.41(2) ϵ implemented continuous dynamical decoupling (CDD) 17 . This generated a set of magnetic field insensitive states 18 , 19 that we denote by , and as they are closely related to the X Y Z states of quantum chemistry 20 rather than the conventional m F angular momentum states. We Raman-coupled atoms prepared in any of the x y z states using the three cross-polarized ‘Raman’ laser beams shown in Fig.…”

Unconventional topology with a Rashba spin-orbit coupled quantum gas

“…An RF magnetic field oscillating at the Larmor frequency with strength Ω RF = 1.41(2) 1 implemented continuous dynamical decoupling (CDD) 24 . This generated a set of magnetic field insensitive states 25,26 that we denote by |x , |y and |z as they are closely related to the XY Z states of quantum chemistry 27 rather than the conventional m F angular momentum states. We Raman-coupled atoms prepared in any of the xyz states using the three cross-polarized 'Raman' laser beams shown in Fig.…”