We study experimentally the fundamental limits of sensitivity of an atomic radio-frequency magnetometer. First we apply an optimal sequence of state preparation, evolution, and the back-action evading measurement to achieve a nearly projection noise limited sensitivity. We furthermore experimentally demonstrate that Einstein-Podolsky-Rosen (EPR) entanglement of atoms generated by a measurement enhances the sensitivity to pulsed magnetic fields. We demonstrate this quantum limited sensing in a magnetometer utilizing a truly macroscopic ensemble of 1.5 · 10 12 atoms which allows us to achieve sub-femtoTesla/ √ Hz sensitivity.Ultra-sensitive atomic magnetometry is based on the measurement of the polarization rotation of light transmitted through an ensemble of atoms placed in the magnetic field [1]. For N A atoms in a state with the magnetic quantum number m F = F along a quantization axis x the collective magnetic moment (spin) of the ensemble has the length J x = F N A . A magnetic field along the y axis causes a rotation of J in the x − z plane. Polarization of light propagating along z will be rotated proportional to J z due to the Faraday effect. From a quantum mechanical point of view, this measurement is limited by quantum fluctuations (shot noise) of light, the projection noise (PN) of atoms, and the quantum backaction noise of light onto atoms. PN originates from the Heisenberg uncertainty relation δJ z · δJ y ≥ J x /2, and corresponds to the minimal transverse spin variances δJ 2 z,y = J x /2 = F N A /2 for uncorrelated atoms in a coherent spin state [2]. Quantum entanglement leads to the reduction of the atomic noise below PN and hence is capable of enhancing the sensitivity of metrology and sensing as discussed theoretically in [2][3][4][5][6][7][8][9]. In [10,11] entanglement of a few ions have been used in spectroscopy. Recently proof-of-principle measurements with larger atomic ensembles, which go beyond the PN limit have been implemented in interferometry with 10 3 atoms [12], in Ramsey spectroscopy [13,14] with up to 10 5 atoms, and in Faraday spectroscopy with 10 6 spin polarized cold atoms [15].In this Letter we demonstrate PN limited and entanglement-assisted measurement of a radio-frequency (RF) magnetic field by an atomic caesium vapour magnetometer. In the magnetometer J precesses at the Larmor frequency Ω/2π = 322kHz around a dc field B = 0.92G applied along the x axis and an RF field with the frequency Ω is applied in the y − z plane (Fig. 1a). The magnetometer (Fig. 2a) detects an RF pulse with a constant amplitude B RF and duration τ (Fourier limited full width half maximum bandwidth δ = 0.88τ −1 ≈ τ −1 ). The mean value of the projection of the atomic spin on the y − z plane in the rotating frame after the RF pulse is ΓB RF J x T 2 [1 − exp(−τ /T 2 )]/2. Here T 2 is the spin decoherence time during the RF pulse and Γ = Ω/B = 2.2 · 10 10 rad/(sec·Tesla) for caesium. Equating the mean value to the PN uncertainty we get for the minimal detectable field under the PN limited measurementThe PN...

Our Letter ''Quantum Noise Limited and Entanglement-Assisted Magnetometry'' by W. Wasilewski et al. contained a reference to M. Koschorreck, M. Napolitano, B. Dubost, and M. Mitchell, arXiv:0911.449. This reference contained a misprint and should read M. Koschorreck, M. Napolitano, B. Dubost, and M. Mitchell, arXiv:0911.4491. We regret this unfortunate error. This Letter has also appeared in press [1]. [1] M. Koschorreck, M. Napolitano, B. Dubost, and M. W. Mitchell, Phys. Rev. Lett. 104, 093602 (2010).

Quantum mechanics dictates that a continuous measurement of the position of an object imposes a random quantum back-action (QBA) perturbation on its momentum. This randomness translates with time into position uncertainty, thus leading to the well known uncertainty on the measurement of motion. As a consequence of this randomness, and in accordance with the Heisenberg uncertainty principle, the QBA puts a limitation-the so-called standard quantum limit-on the precision of sensing of position, velocity and acceleration. Here we show that QBA on a macroscopic mechanical oscillator can be evaded if the measurement of motion is conducted in the reference frame of an atomic spin oscillator. The collective quantum measurement on this hybrid system of two distant and disparate oscillators is performed with light. The mechanical oscillator is a vibrational 'drum' mode of a millimetre-sized dielectric membrane, and the spin oscillator is an atomic ensemble in a magnetic field. The spin oriented along the field corresponds to an energetically inverted spin population and realizes a negative-effective-mass oscillator, while the opposite orientation corresponds to an oscillator with positive effective mass. The QBA is suppressed by -1.8 decibels in the negative-mass setting and enhanced by 2.4 decibels in the positive-mass case. This hybrid quantum system paves the way to entanglement generation and distant quantum communication between mechanical and spin systems and to sensing of force, motion and gravity beyond the standard quantum limit.

We demonstrate lifetimes of atomic populations and coherences in excess of 60 seconds in alkali vapor cells with inner walls coated with an alkene material. This represents two orders of magnitude improvement over the best paraffin coatings. Such anti-relaxation properties will likely lead to substantial improvements in atomic clocks, magnetometers, quantum memory, and enable sensitive studies of collisional effects and precision measurements of fundamental symmetries. [7,8], and precision measurements of fundamental symmetries [9]. One method for achieving long coherence times is to coat the walls of a cell with an anti-relaxation film such as paraffin [10,11] or octadecyltrichlorosilane [12]. Conventional paraffin coatings are formed from long-chain alkane molecules, supporting approximately 10 4 atom-wall collisions before depolarizing the alkali spins. In this Letter we report on the remarkable anti-relaxation properties of a new, alkene based, coating. With proper experimental arrangements, we realize coherence lifetimes on the order of 1 minute in a 3 cm diameter cell, corresponding to about 10 6 polarization preserving bounces. To the best of our knowledge, this corresponds to the narrowest electron paramagnetic resonance ever observed.One of the key ingredients to realizing such long lifetimes is to work in magnetic fields such that the Larmor precession frequency is small compared to the spinexchange rate, and to optically pump the alkali vapor with circularly polarized light. This largely eliminates relaxation due to spin-exchange collisions, the so called spin-exchange relaxation-free (SERF) regime [13,14]. SERF magnetometers presently hold the record for magnetic field sensitivity of any device [15,16], but usually require operation at temperatures in excess of 150• C. The alkene coating described here enables operation of such a magnetometer in a room temperature environment, dramatically expanding its useful range of application, especially where low power consumption is important. We present an experimental and theoretical investigation of a room temperature atomic magnetometer operating in the SERF regime. Experiment and theory are in good agreement with each other.Exchange of atoms between the bulb of the cell and the stem with the Rb reservoir (Fig.