State estimation: direct state measurement vs. tomography

We compare direct state measurement (DST or weak state tomography) to conventional state reconstruction (tomography) through accurate Monte-Carlo simulations. We show that DST is surprisingly robust to its inherent bias. We propose a method to estimate such bias (which introduces an unavoidable error in the reconstruction) from the experimental data. As expected we find that DST is much less precise than tomography. We consider both finite and infinite-dimensional states of the DST pointer, showing that they provide comparable reconstructions.Comment: 4 pages, 4 figure

Linear Stability Analysis of a Levitated Nanomagnet in a Static Magnetic Field: Quantum Spin Stabilized Magnetic Levitation

We theoretically study the levitation of a single magnetic domain nanosphere in an external static magnetic field. We show that apart from the stability provided by the mechanical rotation of the nanomagnet (as in the classical Levitron), the quantum spin origin of its magnetization provides two additional mechanisms to stably levitate the system. Despite of the Earnshaw theorem, such stable phases are present even in the absence of mechanical rotation. For large magnetic fields, the Larmor precession of the quantum magnetic moment stabilizes the system in full analogy with magnetic trapping of a neutral atom. For low magnetic fields, the magnetic anisotropy stabilizes the system via the Einstein-de Haas effect. These results are obtained with a linear stability analysis of a single magnetic domain rigid nanosphere with uniaxial anisotropy in a Ioffe-Pritchard magnetic field.Comment: Published version. 10 pages, 4 figures, 3 table

Quantum Spin Stabilized Magnetic Levitation

We theoretically show that, despite Earnshaw's theorem, a non-rotating single magnetic domain nanoparticle can be stably levitated in an external static magnetic field. The stabilization relies on the quantum spin origin of magnetization, namely the gyromagnetic effect. We predict the existence of two stable phases related to the Einstein--de Haas effect and the Larmor precession. At a stable point, we derive a quadratic Hamiltonian that describes the quantum fluctuations of the degrees of freedom of the system. We show that in the absence of thermal fluctuations, the quantum state of the nanomagnet at the equilibrium point contains entanglement and squeezing.Comment: Published version. 5 pages, 2 figure

Atomic waveguide QED with atomic dimers

Quantum emitters coupled to a waveguide is a paradigm of quantum optics, whose essential properties are described by waveguide quantum electrodynamics (QED). We study the possibility of observing the typical features of the conventional waveguide QED scenario in a system where the role of the waveguide is played by a one-dimensional subwavelength atomic array. For the role of emitters, we propose to use anti-symmetric states of atomic dimers - a pair of closely spaced atoms - as effective two-level systems, which significantly reduces the effect of free-space spontaneous emission. We solve the dynamics of the system both when the dimer frequency lies inside and when it lies outside the band of modes of the array. Along with well-known phenomena of collective emission into the guided modes and waveguide mediated long-range dimer-dimer interactions, we uncover significant non-Markovian corrections which arise from both the finiteness of the array and through retardation effects.Comment: 16 pages, 7 figure

Spin Read-out of the Motion of Levitated Electrically Rotated Diamonds

Recent advancements with trapped nano- and micro-particles have enabled the exploration of motional states on unprecedented scales. Rotational degrees of freedom stand out due to their intrinsic non-linearity and their coupling with internal spin degrees of freedom, opening up possibilities for gyroscopy and magnetometry applications and the creation of macroscopic quantum superpositions. However, current techniques for fast and reliable rotation of particles with internal spins face challenges, such as optical absorption and heating issues. Here, to address this gap, we demonstrate electrically driven rotation of micro-particles levitating in Paul traps. We show that micro-particles can be set to rotate stably at 150,000 rpm by operating in a hitherto unexplored parametrically driven regime using the particle electric quadrupolar moment. Moreover, the spin states of nitrogen-vacancy centers in diamonds undergoing full rotation were successfully controlled, allowing accurate angular trajectory reconstruction and demonstrating high rotational stability over extended periods. These achievements mark progress toward interfacing full rotation with internal magnetic degrees of freedom in micron-scale objects. In particular, it extends significantly the type of particles that can be rotated, such as ferromagnets, which offers direct implications for the study of large gyromagnetic effects at the micro-scale

Spin-Controlled Quantum Interference of Levitated Nanorotors

International audienceWe describe how to prepare an electrically levitated nanodiamond in a superposition of orientations via microwave driving of a single embedded nitrogen-vacancy (NV) center. Suitably aligning the magnetic field with the NV center can serve to reach the regime of ultrastrong coupling between the NV and the diamond rotation, enabling single-spin control of the particle’s three-dimensional orientation. We derive the effective spin-oscillator Hamiltonian for small amplitude rotation about the equilibrium configuration and develop a protocol to create and observe quantum superpositions of the particle orientation. We discuss the impact of decoherence and argue that our proposal can be realistically implemented with near-future technology

Spin Read-out of the Motion of Levitated Electrically Rotated Diamonds

International audienceRecent advancements with trapped nano- and micro-particles have enabled the exploration of motional states on unprecedented scales. Rotational degrees of freedom stand out due to their intrinsic non-linearity and their coupling with internal spin degrees of freedom, opening up possibilities for gyroscopy and magnetometry applications and the creation of macroscopic quantum superpositions. However, current techniques for fast and reliable rotation of particles with internal spins face challenges, such as optical absorption and heating issues. Here, to address this gap, we demonstrate electrically driven rotation of micro-particles levitating in Paul traps. We show that micro-particles can be set to rotate stably at 150,000 rpm by operating in a hitherto unexplored parametrically driven regime using the particle electric quadrupolar moment. Moreover, the spin states of nitrogen-vacancy centers in diamonds undergoing full rotation were successfully controlled, allowing accurate angular trajectory reconstruction and demonstrating high rotational stability over extended periods. These achievements mark progress toward interfacing full rotation with internal magnetic degrees of freedom in micron-scale objects. In particular, it extends significantly the type of particles that can be rotated, such as ferromagnets, which offers direct implications for the study of large gyromagnetic effects at the micro-scale