Single-atom quantum control of macroscopic mechanical oscillators

Until very recently a single atom interacting with an electromagnetic field could only be a topic of theoretical consideration because experimentally only ensembles of atoms were accessible. Atomic spectra and the probabilities of transitions in atoms had been successfully studied in atomic ensembles for a long time. Quantum mechanics enables one to calculate both spectra and probabilities. However, quantum mechanics predicts that any transition happens at a random moment of time. In accordance with this prediction a single atom irradiated by light will make random jumps between its ground and excited electronic states. However, these jumps cannot be observed if we detect emission from the whole atomic ensemble, because a statistical average hides the random character of the processes. Therefore they cannot be observed in ensembles. This is only one example of new aspects which emerge when we move from atomic ensembles to a single atom. In this book we intend to discuss not only problems of probabilistic and spectral calculations, but also various random characteristics of atoms and molecules, the so-called quantum trajectories, which are typical in the spectroscopy of single atoms or molecules. In order to prepare for the discussion of quantum trajectories, we have to discuss the basic principles underlying the spectroscopy of a single two-level atom interacting with a transverse electromagnetic field.

Optomechanics Cooling objects to low temperature can increase the sensitivity of sensors and the operational performance of most devices. Removing most of the thermal vibrations—or phonons—such that the object reaches its motional quantum ground state has been achieved but typically with tiny, nanoscale objects. Using the suspended mirrors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) that form a 10-kg optomechanical oscillator, Whittle et al. demonstrate the ability to cool such a large-scale object to nearly the motional ground state. An upgrade to LIGO with such a modification could increase its sensitivity and range to gravitational waves but also extend studies of quantum mechanics to large-scale objects. Science , abh2634, this issue p. [1333][1] [1]: /lookup/doi/10.1126/science.abh2634

Summary form only given. Thermal mechanical motion hinders the use of a mechanical system in applications such as quantum information processing. A straightforward, but technically challenging, approach to overcome the thermal motion is to cool the mechanical oscillator to its motional ground state. An alternative approach, as proposed recently, is to exploit the use of a mechanically-dark mode, which is a special coherent superposition of two optical modes [1, 2]. The cancellation in the mechanical coupling induced by the superposition decouples the dark mode from the mechanical oscillator. The formation of the dark mode, however, also induces a conversion of the optical field from one optical mode to the other. This type of mechanically-mediated coupling is immune to thermal mechanical motion, providing a promising mechanism for interfacing hybrid quantum systems. Here, we report the experimental demonstration of such a dark mode by coupling two optical modes in a silica resonator to one of its mechanical breathing modes in the regime of weak optomechanical coupling [3].

Quantum squeezing in macroscopic oscillator systems plays a critical role in bridging quantum mechanics with classical-scale phenomena, enabling high-precision measurements and fundamental tests of quantum physics. In this work, we investigate the effect of squeezing on the phonon state in a hybrid macroscopic mechanical system consisting of an ensemble of Rydberg atoms coupled to two macroscopic mechanical oscillators. We notice that the dipole–dipole coupling between atoms and mechanical oscillators can be transferred to the indirectly coupled mechanical interaction, and the nonlinear effective Hamiltonian can be solved to generate a squeezed effect on the mechanical mode. We also discuss the noise effects induced by amplitude and phase fluctuations on the squeezed quadratures of the system.

Localization to the ground state of axial motion is demonstrated for a single, trapped atom strongly coupled to the field of a high finesse optical resonator. The axial atomic motion is cooled by way of coherent Raman transitions on the red vibrational sideband. An efficient state detection scheme enabled by strong coupling in cavity QED is used to record the Raman spectrum, from which the state of atomic motion is inferred. We find that the lowest vibrational level of the axial potential with zero-point energy variant Planck's over 2 h omega a/2kB = 13 microK is occupied with probability P0 approximately 0.95.

Conventional laser cooling techniques have proved inefficient on mechani-cal oscillators heavier than a few nanograms. Here, we present a new approach to realize motional ground state cooling of such oscillators, paving the way to currently inaccessible experiments such as tests of gravity’s effect on massive quantum systems.

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 the formation of a single NaCs molecule in an optical tweezer by magnetoassociation through an s-wave Feshbach resonance at 864.11(5)G. Starting from single atoms cooled to their motional ground states, we achieve conversion efficiencies of 47(1)%, and measure a molecular lifetime of 4.7(7)ms. By construction, the single molecules are predominantly [77(5)%] in the center-of-mass motional ground state of the tweezer. Furthermore, we produce a single p-wave molecule near 807G by first preparing one of the atoms with one quantum of motional excitation. Our creation of a single weakly bound molecule in a designated internal state in the motional ground state of an optical tweezer is a crucial step towards coherent control of single molecules in optical tweezer arrays.

In contrast to current efforts to quantify the radiation pressure of light using nano-micromechanical resonators in cryogenic conditions, we proposed and experimentally demonstrated the radiation pressure measurement in ambient conditions by utilizing a macroscopic mechanical longitudinal oscillator with an effective mass of the order of 20 g. The light pressure on a mirror attached to the oscillator was recorded in a Michelson interferometer and results showed, within the experimental accuracy of 3.9%, a good agreement with the harmonic oscillator model without free parameters.

Is an atom more likely to scatter a photon with an exponentially rising or decaying temporal profile? We try to answer this question experimentally and investigate the scattering of heralded photons from a single atom in free-space [1]. We use a single Rubidium atom trapped in optical tweezers and prepared in the groundstate of a cyclic dipole transition as a textbook-like two-level system. A time-ordered photon pair source, in conjunction with an asymmetric cavity, generates heralded single photons with an exponentially decaying or rising temporal profile [2, 3]. The heralded photons are resonant with the atomic transition and have a bandwidth comparable to the atomic linewidth. The photons are strongly focused onto the atom by a large numerical aperture lens. We study the scattering dynamics by measuring the atomic emission and the reduction in the number of transmitted photons. We perform the scattering experiment for photons with exponentially decaying and rising temporal envelopes and find that the atomic dynamics depend on the temporal profile of the photon. The atomic absorption is shorter but has a higher maximum for the rising photon than for the the decaying one. Interestingly, the overall probability that the photon is scattered by the atom is similar for decaying and rising photons.

We demonstrate full quantum state control of two species of single atoms using optical tweezers and assemble the atoms into a molecule. Our demonstration includes 3D ground-state cooling of a single atom (Cs) in an optical tweezer, transport by several microns with minimal heating, and merging with a single Na atom. Subsequently, both atoms occupy the simultaneous motional ground state with 61(4)\% probability. This realizes a sample of exactly two co-trapped atoms near the phase-space-density limit of one, and allows for efficient stimulated-Raman transfer of a pair of atoms into a molecular bound state of the triplet electronic ground potential $a^3\Sigma^+$. The results are key steps toward coherent creation of single ultracold molecules, for future exploration of quantum simulation and quantum information processing.

A promising route to novel quantum technologies are hybrid quantum systems, which combine the advantages of several individual quantum systems. We have realized a hybrid atomic-mechanical experiment consisting of a Si3N4 membrane oscillator cryogenically precooled to 500 mK and optically coupled to a cloud of laser cooled 87Rb atoms. Here, we demonstrate active feedback cooling of the oscillator to a minimum mode occupation of corresponding to a mode temperature of Tmin ≈ 200 μK. Furthermore, we characterize in detail the coupling of the membrane to the atoms by means of sympathetic cooling. By simultaneously applying both cooling methods we demonstrate the possibility of preparing the oscillator near the motional ground state while it is coupled to the atoms. Realistic modifications of our setup will enable the creation of a ground state hybrid quantum system, which opens the door for coherent quantum state transfer, teleportation and entanglement as well as quantum enhanced sensing applications.

We investigate the influence of laser phase noise heating on resolved sideband cooling in the context of cooling the center-of-mass motion of a levitated nanoparticle in a high-finesse cavity. Although phase noise heating is not a fundamental physical constraint, the regime where it becomes the main limitation in Levitodynamics has so far been unexplored and hence embodies from this point forward the main obstacle in reaching the motional ground state of levitated mesoscopic objects with resolved sideband cooling. We reach minimal center-of-mass temperatures comparable to T_{min}=10 mK at a pressure of p=3×10^{-7} mbar, solely limited by phase noise. Finally we present possible strategies towards motional ground state cooling in the presence of phase noise.

Trapped ions provide a highly controlled platform for quantum sensors, clocks, simulators, and computers, all of which depend on cooling ions close to their motional ground state. Existing methods like Doppler, resolved sideband, and dark resonance cooling balance trade-offs between the final temperature and cooling rate. A traveling polarization gradient has been shown to cool multiple modes quickly and in parallel, but utilizing a stable polarization gradient can achieve lower ion energies, while also allowing tailorable light-matter interactions in the sub-wavelength regime. In this Letter, we demonstrate cooling of a trapped ion below the Doppler limit using a phase-stable polarization gradient created using trap-integrated photonic devices. At an axial frequency of 2π×1.45 MHz we achieve ⟨n⟩=1.56±0.07 in 150 μs and cooling rates of ∼0.3 quanta/μs. We examine ion dynamics under different polarization gradient phases, detunings, and intensities, showing reasonable agreement between experimental results and a multilevel model. Cooling is fast and power efficient, with lower average motional Fock state occupation when compared to simulated operation under the corresponding running wave configuration. Our results demonstrate a well-controlled test bed for studying the dynamics of multilevel atomic systems in a phase-stable polarization gradient.

The entanglement of macroscopic mechanical oscillators is always an interesting domain. How to entangle multiple mechanical oscillators is still not well answered. In this paper, we investigate the bipartite and tripartite quantum correlations among three distinct mechanical oscillators interacting with one cavity pumped by a multi-tone driving laser. Floquet cavity modes, resulting from different frequency components of the multi-tone driven cavity, are used to construct channels for quantum correlations between mechanical oscillators. By modulating the effective optomechanical coupling, we can manipulate the mechanical entanglement and EPR steering. The numerical results show that the two-tone driving widely employed is not enough to generate tripartite entanglement, while three- and four-tone driving can be employed to generate and enhance genuine tripartite entanglement. All bipartite entanglement can also be modulated. In addition, we demonstrate the monogamous relation of tripartite EPR steering and manipulate the asymmetry of steering. This work provides a method for manipulating the quantum correlation among multiple macroscopic objects.