ARTICLE Received 1 Nov 2012 | Accepted 26 Nov 2012 | Published 27 Dec 2012 DOI: 10.1038/ncomms2332 Ultrasensitive magnetic field detection using a single artificial atom M. Bal1, C. Deng1, J.-L. Orgiazzi2, F.R. Ong1 & A. Lupascu1 Efficient detection of magnetic fields is central to many areas of research and technology. High-sensitivity detectors are commonly built using direct-current superconducting quantum interference devices or atomic systems. Here we use a single artificial atom to implement an ultrasensitive magnetometer with micron range size. The artificial atom, a superconducting two-level system, is operated similarly to atom and diamond nitrogen-vacancy centre-based magnetometers. The high sensitivity results from quantum coherence combined with strong coupling to magnetic field. We obtain a sensitivity of 3.3 pT Hz À 1/2 for a frequency of 10 MHz. We discuss feasible improvements to increase sensitivity by one order of magnitude. The intrinsic sensitivity of this detector at frequencies in the 100 kHz–10 MHz range com- pares favourably with direct-current superconducting quantum interference devices and atomic magnetometers of equivalent spatial resolution. This result illustrates the potential of artificial quantum systems for sensitive detection and related applications. 1Institute for Quantum Computing, Department of Physics and Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. 2Institute for Quantum Computing, Department of Electrical and Computer Engineering, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. Correspondence and requests for materials should be addressed to A.L. (email: [email protected]). NATURE COMMUNICATIONS | 3:1324 | DOI: 10.1038/ncomms2332 | www.nature.com/naturecommunications 1 & 2012 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms2332 ensitive physical measurements are an essential component in typical atomic systems. The lower coherence time is unfavourable of modern science and technology. In particular, detection for sensitive detection. However, this drawback is compensated for Sof magnetic fields is an area of wide interest, with various by the large coupling to magnetic field, typically five orders of applications including medical imaging, geomagnetics, non- magnitude larger than in atomic systems. To optimize magnetic field destructive materials evaluation, scanning probe microscopy, detection sensitivity, we use an operation mode based on detection and electrical measurements1,2. Magnetic field sensors are also of correlation of qubit measurement results. We find a sensitivity of enabling tools for fundamental studies of magnetism3, spin 3.3 pT Hz À 1/2 for operation at 10 MHz. The detection bandwidth dynamics4, fundamental symmetries2 and mechanical motion5,6. around a centre frequency of 8 MHz reaches 1 MHz, limited at Sensitive tools to detect magnetic fields are diverse and include present by the overhead time introduced by measurement. The direct-current superconducting quantum interference devices measured sensitivity is comparable with state of the art (DC-SQUIDs)1, atomic magnetometers2, Hall probes7 and magnetometers based on DC-SQDUIDs or atoms/NV centres of magnetostrictive sensors8. DC-SQUIDs have been established equivalent spatial resolution. We present a theoretical analysis which for a long time as very sensitive magnetometers1. In recent years, showsthatoneorderofmagnitudefurtherimprovementispossible significant advances in atomic control led to the development of with feasible changes in the detection scheme. Our results atomic magnetometers, which presently compete with DC- demonstrate the potential of artificial quantum systems for high- SQUIDs for magnetic field detection and have the convenience sensitivity low-backaction detection. of operation in a room temperature environment2. Atomic magnetometers rely on the measurement of the effect of the field on the coherent dynamics of an ensemble of atoms. A detection Results method similar to atomic magnetometry can be implemented Coherent control and measurement of the qubit state. The using nitrogen-vacancy defects (NV centres) in diamond artificial atom used in our experiments for magnetic field detec- crystals9. Magnetometers based on single NV centres10,11 have tion, a PCQ, is a superconducting loop with three Josephson been demonstrated and shown to have interesting prospects as junctions, shown in Fig. 1. The qubit is operated in a dilution high-spatial-resolution high-sensitivity detectors. refrigerator at a temperature of 43 mK. The qubit Hamiltonian is hD s F F s F The principle of our approach follows closely that of given by Hqb ¼À 2 x À Ipð À 0/2Þ z, where is the mag- magnetometry based on vapour cells or NV centres2,9. The netic flux applied to the qubit ring, F0 ¼ h/2e is the flux quantum, method employs a Ramsey interferometry sequence. The first step and hD is the minimum energy-level splitting of the qubit, which is initialization of the spin in a superposition of the up and down occurs at the symmetry point F ¼ F0/2 (see Fig. 1d). This states with respect to a reference axis. Precession due to an representation of the Hamiltonian uses two states with persistent current ±I flowing in the qubit ring. The effective magnetic applied magnetic field for a durationR t around time t leads to an p 1 t þ t/2 0 0 m dnge n accumulated phase fðt; tÞ¼ h t À t/2 mBðt Þdt , with m the moment of the qubit is ¼ h dB with h ge the energy-level magnetic moment and B(t) the time-dependent component of difference between the excited (e) and ground (g) states and the magnetic field along the reference axis. Next, the spin is B ¼ F/Aqb the magnetic field applied to the qubit ring; Aqb is the rotated with a coherent control pulse, so that the projection along qubitpffiffiffiffiffiffiffiffiffiffiffiffi loop area. The magnetic moment is given by 2 2 the reference axis depends on f(t, t), hence on the magnetic field. nge À D m ¼ 2IpAqb. For our qubit, characterized by Ip ¼ 140 nA, A single measurement produces a result r ¼ ±1, corresponding nge 2 to the two spin states. For N repetitions of the sequence, the Aqb ¼ 24.5 mm and D ¼ 9.82 GHz, and operated at nge ¼ 11.39 5 average value of the measurement /rS ¼ sinf and the standard GHz, m reaches the value 3.8  10 mB. This large magnetic deviation is 1/ON. The minimum detectable magnetic field moment enables a large sensitivity, despite the coherence time of the PCQ being shorter than in typical atomic systems2,9. We note difference, correspondingffiffiffiffi to a signal to noise ratio ofq 1,ffiffiffiffiffiffi is p T that a different method to use a PCQ for magnetometry, based on dB ¼ h/ mt N. This can be expressed as dB ¼ h p1ffiffiffiffi rep, min min m tT t susceptibility of a qubit as opposed to quantum coherent with Trep the repetition time of the procedure described above dynamics, was discussed in ref. 14; the predicted sensitivity is and T ¼ NTrep the total measurement time.pffiffiffiffi The sensitivity can lower than for the detection scheme we discuss here. thus be expressed as the quantity dBmin T, which has units of Control of the state of the PCQ is done by an applied À 1/2 THz . The sensitivity increases with the time t as long as the magnetic flux F. We bias the qubit with a flux F(t) ¼ Fb þ dF(t), evolution is fully coherent; with decoherence taken into account, where Fb is a static bias flux produced by an external the optimum is reached when t is of the order of the Ramsey coil and dF(t) is a fast varying flux coupled to the qubit * coherence time T2. via a coplanar waveguide terminated by an inductance In existing magnetometers based on this principle, the two spin (see Fig. 1a,b). We can write the qubit Hamiltonian as 2 hnge states of interest are hyperfine or Zeeman levels in alkali atoms HqbðtÞ¼ À tz À IpdFðtÞð À cos Ebtx þ sin EbtzÞ, where tx 9 2 or spin sublevels of the ground state in NV centres in diamond . and tz are Pauli operators in the energy eigenbasis Detection is done most commonly using an ensemble of atoms/ and Eb ¼ arctan(Ip(Fb À F0/2)/(hD)). Coherent qubit control is defects.pffiffiffiffi WithpNffiffiffiffiffiffiat atoms, sensitivity is further enhanced by a factor implemented by applying a flux dF(t) ¼ dF0(t)cos(2pnget À b(t)) 1/ Nat ¼ 1/ pVnffiffiffiffi, with V the volume and n the density of the with the amplitude dF0(t) and the phase b(t) slow (compared À 1 cloud. The 1/ V dependence of sensitivity implies that there is a with nge ) functions of time. In the frame rotating at tradeoff between sensitivity and spatial resolution. The same the qubit frequency, the Hamiltonian is given by tradeoff also appears in magnetic field sensors based on DC- HqbðtÞ¼Ip cos EbdF0ðtÞ/2t~nðbðtÞÞ. Here t~nðbðtÞÞ is the Pauli SQUIDs1. operator along an axis in the xy plane at an angle b(t) with the In this paper, we demonstrate ultra-high sensitivity detection of x axis. Below, we use y~n to denote a rotation of angle y around an alternating current (AC) magnetic fields using a single artificial axis defined by the vector ~n. atom. The artificial atom is a persistent current qubit (PCQ)—a Quantum measurement of the PCQ state is performed by using micron-sized superconducting ring with Josephson junctions12. a circuit-quantum electrodynamics set-up in the dispersive This system has been studied extensively for quantum computing regime15–18. The qubit is inductively coupled to a applications13. Owing to the interaction with its solid state superconducting resonator, with a resonance frequency environment, the PCQ has a coherence time that is shorter than nres ¼ 6.602 GHz, and quality factor Q ¼ 4,000 defined by 2 NATURE COMMUNICATIONS | 3:1324 | DOI: 10.1038/ncomms2332 | www.nature.com/naturecommunications & 2012 Macmillan Publishers Limited.