Quantum Mechanical Squeezing Enhances Sensing by NIST

Quantum mechanical squeezing, a technique that reduces uncertainty in a desired observable by increasing uncertainty in a separate non-commuting observable, can enhance sensing and measurement. The recently proposed Hamiltonian amplification (HA) method can achieve squeezing-based enhancement where parameters fluctuate or are unknown. Researchers have experimentally realized HA using the motion of a trapped atomic ion as the quantum harmonic oscillator, demonstrating phase-insensitive amplification of coherent displacements of the ion motion. This research, conducted by scientists from various US institutions, could be helpful when certain aspects of a signal or interaction may be unknown or uncontrolled.

What is Quantum Mechanical Squeezing, and How Does it Enhance Sensing and Measurement?

Quantum mechanical squeezing is a technique where the uncertainty in a desired observable is reduced at the expense of increasing uncertainty in a separate non-commuting observable. This technique is a powerful tool for quantum-enhanced sensing and measurement, enabling the detection of extremely weak signals or forces. Squeezing can also enhance the strength of interactions between quantum systems, for example, by amplifying optomechanical or light-matter interactions relevant to quantum information science.

The amount of enhancement in sensitivity or interaction strength that can be achieved depends not just on the strength and fidelity of the squeezing operations but also on their timing and phase relationship relative to the other parameters in the Hamiltonian system, including the signal to be sensed or the interaction to be enhanced. In some applications, the required phases and timings for squeezing operations relative to the rest of the system dynamics may be sufficiently stable that they can be calibrated in advance. However, in other instances, the parameters of the Hamiltonian may be unknown or fluctuate in time, such that naive application of squeezing operations can give rise to undesired error dynamics in the system in addition to the desired enhancement.

How Does Hamiltonian Amplification Work?

The recently proposed scheme of Hamiltonian amplification (HA) provides a method to achieve squeezing-based enhancement of dynamics involving a quantum harmonic oscillator where parameters are fluctuating or unknown. By stroboscopically applying squeezing transformations with alternating phases, errors due to unknown phase relationships are dynamically suppressed while the desired interactions are strengthened or amplified. Crucially, the protocol does not require knowledge of the parameters of the Hamiltonian to be amplified, as long as it can be written in a certain form and the timescales for the bare Hamiltonian dynamics are slow compared to the duration of applied squeezing operations.

In this work, the researchers experimentally realized Hamiltonian amplification using the motion of a trapped atomic ion as the quantum harmonic oscillator. As proof of principle, they used HA to demonstrate phase-insensitive amplification of coherent displacements of the ion motion with a gain of approximately 2 as the relative phase of the displacement is swept across the full range of 2 π. They also performed phase-insensitive enhancement of laser-induced coupling between the trapped ion’s motion and its internal electronic spin state, where the phase of the laser interaction is not stable with respect to that of the squeezing interaction, observing an increase in the effective spin-motion coupling strength of approximately 1.5.

What is the Theoretical Background of Quantum Harmonic Oscillator?

The coupling of a particular quantum harmonic oscillator with Hamiltonian to another quantum system or to an external resonant driving field that results in a signal to be sensed can be described in the interaction picture concerning the bare oscillator Hamiltonian and all terms not involving the chosen harmonic oscillator by a Hamiltonian of a certain form. Here, the annihilation and creation operators of the chosen harmonic oscillator, the harmonic oscillator frequency, and the interaction strength with either an external driving field or a second quantum system are all factors.

For example, in the case where the lowering operator for a two-level system represented by a spin-1/2 particle, the operator describing the second quantum system does not need to be specified for the HA procedure to work, which makes the method amenable to amplifying interactions in a wide range of systems. This is true even when the operator is unknown, for example in the case of searches for novel forms of dark matter.

What are the Implications of this Research?

This research shows experimentally that a broad class of interactions involving quantum harmonic oscillators can be made stronger or amplified using a unitary squeezing protocol. While the demonstration uses the motional and internal states of a single trapped ion, the scheme applies generally to Hamiltonians involving just a single harmonic oscillator, as well as Hamiltonians coupling the oscillator to another quantum degree of freedom such as a qubit, covering a large range of systems of interest in quantum information and metrology applications.

Importantly, the protocol does not require knowledge of the parameters of the Hamiltonian to be amplified, nor does it require a well-defined phase relationship between the squeezing interaction and the rest of the system dynamics, making it potentially useful in instances where certain aspects of a signal or interaction may be unknown or uncontrolled, such as searches for novel forms of dark matter.

This research was conducted by a team of scientists from the Time and Frequency Division National Institute of Standards and Technology, the Department of Physics at the University of Colorado, the School of Electrical Computer and Energy Engineering at Arizona State University, and the Department of Physics at the University of Oregon. The findings were published in the American Physical Society journal.