Low-loss transmission and sensitive recovery of weak radio-frequency and microwave signals is a ubiquitous challenge, crucial in radio astronomy, medical imaging, navigation, and classical and quantum communication. Efficient up-conversion of radio-frequency signals to an optical carrier would enable their transmission through optical fibres instead of through copper wires, drastically reducing losses, and would give access to the set of established quantum optical techniques that are routinely used in quantum-limited signal detection. Research in cavity optomechanics has shown that nanomechanical oscillators can couple strongly to either microwave or optical fields. Here we demonstrate a room-temperature optoelectromechanical transducer with both these functionalities, following a recent proposal using a high-quality nanomembrane. A voltage bias of less than 10 V is sufficient to induce strong coupling between the voltage fluctuations in a radio-frequency resonance circuit and the membrane's displacement, which is simultaneously coupled to light reflected off its surface. The radio-frequency signals are detected as an optical phase shift with quantum-limited sensitivity. The corresponding half-wave voltage is in the microvolt range, orders of magnitude less than that of standard optical modulators. The noise of the transducer--beyond the measured 800 pV Hz-1/2 Johnson noise of the resonant circuit--consists of the quantum noise of light and thermal fluctuations of the membrane, dominating the noise floor in potential applications in radio astronomy and nuclear magnetic imaging. Each of these contributions is inferred to be 60 pV Hz-1/2 when balanced by choosing an electromechanical cooperativity of ~150 with an optical power of 1 mW. The noise temperature of the membrane is divided by the cooperativity. For the highest observed cooperativity of 6,800, this leads to a projected noise temperature of 40 mK and a sensitivity limit of 5 pV Hz-1/2. Our approach to all-optical, ultralow-noise detection of classical electronic signals sets the stage for coherent up-conversion of low-frequency quantum signals to the optical domain.

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.

The relation between substrate and water transport was studied in Na + -coupled cotransporters of glucose (SGLT1) and of iodide (NIS) expressed in Xenopus oocytes. The water transport was monitored from changes in oocyte volume at a resolution of 20 pl, more than one order of magnitude better than previous investigations. The rate of cotransport was monitored as the clamp current obtained from two-electrode voltage clamp. The high resolution data demonstrated a fixed ratio between the turn-over of the cotransporter and the rate of water transport. This applied to experiments in which the rate of cotransport was changed by isosmotic application of substrate, by rapid changes in clamp voltage, or by poisoning. Transport of larger substrates gave rise to less water transport. For the rabbit SGLT1, 378 ± 20 (n = 18 oocytes) water molecules were cotransported along with the 2 Na + ions and the glucose-analogue α-MDG (MW 194); using the larger sugar arbutin (MW 272) this number was reduced by a factor of at least 0.86 ± 0.03 (15). For the human SGLT1 the respective numbers were 234 ± 12 (18) and 0.85 ± 0.8 (7). For NIS, 253 ± 16 (12) water molecules were cotransported for each 2 Na + and 1 thiocyanate (SCN − , MW 58), with I − as anion (MW 127) only 162 ± 11 (19) water molecules were cotransported. The effect of substrate size suggests a molecular mechanism for water cotransport and is opposite to what would be expected from unstirred layer effects. Data were analysed by a model which combined cotransport and osmosis at the membrane with diffusion in the cytoplasm. The combination of high resolution measurements and precise modelling showed that water transport across the membrane can be explained by cotransport of water in the membrane proteins and that intracellular unstirred layers effects are minute.

A model was set up to study water transport in membrane proteins expressed in Xenopus oocytes. The model was tested experimentally using human and rabbit Na+‐glucose cotransporters (SGLT1), and was used to explain controversies regarding unstirred layer effects. Cotransport of Na+, sugar and water was monitored by two‐electrode voltage clamp and online measurements of oocyte volume. The specific resistance of the oocyte cytoplasm was found by means of microelectrodes to be 263 ± 91 Ω cm (s.d., n= 52), or 2.5 times that of Kulori medium, in agreement with reported values of intracellular ion concentrations and diffusion constants. Osmotically induced volume and resistance changes were compatible with a model of the oocyte in which 37 ± 17 % (s.d., n= 66) of the intracellular volume acts as a free solution while the remainder is inert, being occupied by organelles, etc. The model explains the results of several types of experiments: rapid changes in rates of water cotransport induced by changes in clamp voltage followed by osmotic equilibration in sugar‐free conditions; volume changes induced by Na+ transport via the ionophore gramicidin; and uphill water transport. Ethanol (0.5 %) induced a marked swelling of the oocytes of about 16 pl s−1. If the specific inhibitor of SGLT1 phlorizin is added from stock solutions in ethanol, the effect of ethanol obfuscates the effects of the inhibitor. We conclude that the transport parameters derived for water cotransport by the SGLT1 can be attributed to the protein residing in the plasma membrane with no significant influences from unstirred layer effects.

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