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Register a new userDeterministic Ultracold Ion Source targeting the Heisenberg Limit
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The major challenges to fabricate quantum processors and future nano solid state devices are material modification techniques with nanometre resolution and suppression of statistical fluctuations of dopants or qubit carriers. Based on a segmented ion trap with mK laser cooled ions we have realized a deterministic single ion source which could operate with a huge range of sympathetically cooled ion species, isotopes or ionic molecules. We have deterministically extracted a predetermined number of ions on demand and have measured a longitudinal velocity uncertainty of 6.3m/s and a spatial beam divergence of 0.6 mrad. We show in numerical simulations that if the ions are cooled to the motional ground state (Heisenberg limit) nanometre spatial resolution can be achieved.
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We consider the precision $Delta varphi$ with which the parameter $varphi$, appearing in the unitary map $U_varphi = e^{ i varphi Lambda}$ acting on some type of probe system, can be estimated when there is a finite amount of prior information about $varphi$. We show that, if $U_varphi$ acts $n$ times in total, then, asymptotically in $n$, there is a tight lower bound $Delta varphi geq frac{pi}{n (lambda_+ - lambda_-)}$, where $lambda_+$, $lambda_-$ are the extreme eigenvalues of the generator $Lambda$. This is greater by a factor of $pi$ than the conventional Heisenberg limit, derived from the properties of the quantum Fisher information. That is, the conventional bound is never saturable. Our result makes no assumptions on the measurement protocol, and is relevant not only in the noiseless case but also if noise can be eliminated using quantum error correction techniques.
To quantify quantum optical coherence requires both the particle- and wave-natures of light. For an ideal laser beam [1,2,3], it can be thought of roughly as the number of photons emitted consecutively into the beam with the same phase. This number, $mathfrak{C}$, can be much larger than $mu$, the number of photons in the laser itself. The limit on $mathfrak{C}$ for an ideal laser was thought to be of order $mu^2$ [4,5]. Here, assuming nothing about the laser operation, only that it produces a beam with certain properties close to those of an ideal laser beam, and that it does not have external sources of coherence, we derive an upper bound: $mathfrak{C} = O(mu^4)$. Moreover, using the matrix product states (MPSs) method [6,7,8,9], we find a model that achieves this scaling, and show that it could in principle be realised using circuit quantum electrodynamics (QED) [10]. Thus $mathfrak{C} = O(mu^2)$ is only a standard quantum limit (SQL); the ultimate quantum limit, or Heisenberg limit, is quadratically better.
We provide efficient and intuitive tools for deriving bounds on achievable precision in quantum enhanced metrology based on the geometry of quantum channels and semi-definite programming. We show that when decoherence is taken into account, the maximal possible quantum enhancement amounts generically to a constant factor rather than quadratic improvement. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: dephasing,depolarization, spontaneous emission and photon loss.
We propose an approach to quantum phase estimation that can attain precision near the Heisenberg limit without requiring single-particle-resolved state detection. We show that the one-axis twisting interaction, well known for generating spin squeezing in atomic ensembles, can also amplify the output signal of an entanglement-enhanced interferometer to facilitate readout. Applying this interaction-based readout to oversqueezed, non-Gaussian states yields a Heisenberg scaling in phase sensitivity, which persists in the presence of detection noise as large as the quantum projection noise of an unentangled ensemble. Even in dissipative implementations -- e.g., employing light-mediated interactions in an optical cavity or Rydberg dressing -- the method significantly relaxes the detection resolution required for spectroscopy beyond the standard quantum limit.
The use of quantum resources can provide measurement precision beyond the shot-noise limit (SNL). The task of ab initio optical phase measurement---the estimation of a completely unknown phase---has been experimentally demonstrated with precision beyond the SNL, and even scaling like the ultimate bound, the Heisenberg limit (HL), but with an overhead factor. However, existing approaches have not been able---even in principle---to achieve the best possible precision, saturating the HL exactly. Here we demonstrate a scheme to achieve true HL phase measurement, using a combination of three techniques: entanglement, multiple samplings of the phase shift, and adaptive measurement. Our experimental demonstration of the scheme uses two photonic qubits, one double passed, so that, for a successful coincidence detection, the number of photon-passes is $N=3$. We achieve a precision that is within $4%$ of the HL, surpassing the best precision theoretically achievable with simpler techniques with $N=3$. This work represents a fundamental achievement of the ultimate limits of metrology, and the scheme can be extended to higher $N$ and other physical systems.
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