## Periodic Reporting for period 2 - QUANTUM-N (Quantum Mechanics in the Negative Mass Reference Frame)

Reporting period: 2020-01-01 to 2021-06-30

A fundamental aspect of quantum mechanics is the balance between information and disturbance by the measurement. A

textbook example is the measurement of a position of an object which imposes a random perturbation on its momentum.

This perturbation, the quantum back action, translates with time into uncertainty of the motion trajectory. The PI has

proposed an approach which allows for simultaneous measurements of arbitrary small disturbances in both the position

and the momentum. It is based on a measurement performed in a quantum reference frame with an effective negative

mass, or frequency for an oscillator. The PI’s group has experimentally demonstrated the first step along this novel

path - quantum back action evasion for the measurement of motion in a reference frame of a spin oscillator.

This project takes detection of motion to a new frontier. We develop a novel hybrid quantum system

involving disparate macroscopic objects, a mechanical oscillator and a reference spin oscillator with the effective negative

mass. We will demonstrate quantum entanglement between the two oscillators and entanglement-enhanced sensing of

force and acceleration. The technology for high quality mechanical and spin oscillators developed at the PI’s group will be

further advanced towards those goals.

We will generate manifestly non-classical states of millimetre size mechanical oscillators and a macroscopic coherent

superposition of distant spin and mechanical objects. We will furthermore work towards generation of multi-partite

entangled states of spins, macroscopic objects, and photons, thus testing fundamental limits of entanglement and

decoherence for large and complex systems.

Gravitational wave interferometers which have recently detected first gravitational waves are expected to be soon limited in

their sensitivity by the quantum back action. The way to overcome this limit using the approach developed within this

project will be explored.

textbook example is the measurement of a position of an object which imposes a random perturbation on its momentum.

This perturbation, the quantum back action, translates with time into uncertainty of the motion trajectory. The PI has

proposed an approach which allows for simultaneous measurements of arbitrary small disturbances in both the position

and the momentum. It is based on a measurement performed in a quantum reference frame with an effective negative

mass, or frequency for an oscillator. The PI’s group has experimentally demonstrated the first step along this novel

path - quantum back action evasion for the measurement of motion in a reference frame of a spin oscillator.

This project takes detection of motion to a new frontier. We develop a novel hybrid quantum system

involving disparate macroscopic objects, a mechanical oscillator and a reference spin oscillator with the effective negative

mass. We will demonstrate quantum entanglement between the two oscillators and entanglement-enhanced sensing of

force and acceleration. The technology for high quality mechanical and spin oscillators developed at the PI’s group will be

further advanced towards those goals.

We will generate manifestly non-classical states of millimetre size mechanical oscillators and a macroscopic coherent

superposition of distant spin and mechanical objects. We will furthermore work towards generation of multi-partite

entangled states of spins, macroscopic objects, and photons, thus testing fundamental limits of entanglement and

decoherence for large and complex systems.

Gravitational wave interferometers which have recently detected first gravitational waves are expected to be soon limited in

their sensitivity by the quantum back action. The way to overcome this limit using the approach developed within this

project will be explored.

The project specific ground breaking goals and the main results achieved so far:

1). Generation of a range of entangled states of two distant and disparate macroscopic objects, the

mechanical oscillator and the atomic spin oscillator.

We have developed theoretically a novel approach towards entanglement generation between those two macroscopic systems

We have successfully achieved one of the major goals of this project: generation of an entangled state of a mechanical oscillator, a mm-size dielectric membrane and an

atomic spin oscillator built of 100 million atoms.

The entangled state spreads over a meter-scale distance and marks a new frontier in macroscopic entanglement. This work has been published in Nature Physics. and highlighted in by Nature News and Views and other outlets.

2). Demonstration of the measurement of force and acceleration beyond the standard quantum limit

of sensitivity. We have applied the quantum measurement principles developed in the project to various real life applications, such as transduction of

electric and magnetic signals to the optical domain, magnetocardiography on an isolated animal

heart, magnetic resonance imaging and detection of low-conductivity objects with an optical magnetometer.

Theoretical research towards measurements beyond the standard quantum limit continues.

3). Observation of macroscopic superposition states of moving millimetre size objects is fundamental for testing the limits of quantum theory. Towards this goal we have developed an experimental setup where a macroscopic object,

a mm size dielectric membrane, is cooled close to near absolute zero temperature. We then have observed photon scattering signifying the processes of adding

and subtracting a single motional phonon from the membrane. This achievement paves the road towards generation and detection of highly non-classical states of macroscopic objects.

In a parallel effort we have made progress with the demonstration of a single spin excitation in a macroscopic ensembles of room temperature

atoms.

4). Feasibility studies of application of the negative mass idea to multipartite entanglement involving

spins, photons and massive objects such as mirrors of gravitational wave interferometers.

We have made significant steps towards the development of a "negative-mass quantum noise eater" which can be used for the proof-of-principle demonstration of enhanced sensitivity of

gravitational wave interferometers (GWIs), such as LIGO. We have made progress in development of a critical component of this experiment - a source of entangled light which couples to the atomic negative mass system and to the GWI. A new idea paves the way towards experimentally feasible implementation of the negative mass atomic system.

1). Generation of a range of entangled states of two distant and disparate macroscopic objects, the

mechanical oscillator and the atomic spin oscillator.

We have developed theoretically a novel approach towards entanglement generation between those two macroscopic systems

We have successfully achieved one of the major goals of this project: generation of an entangled state of a mechanical oscillator, a mm-size dielectric membrane and an

atomic spin oscillator built of 100 million atoms.

The entangled state spreads over a meter-scale distance and marks a new frontier in macroscopic entanglement. This work has been published in Nature Physics. and highlighted in by Nature News and Views and other outlets.

2). Demonstration of the measurement of force and acceleration beyond the standard quantum limit

of sensitivity. We have applied the quantum measurement principles developed in the project to various real life applications, such as transduction of

electric and magnetic signals to the optical domain, magnetocardiography on an isolated animal

heart, magnetic resonance imaging and detection of low-conductivity objects with an optical magnetometer.

Theoretical research towards measurements beyond the standard quantum limit continues.

3). Observation of macroscopic superposition states of moving millimetre size objects is fundamental for testing the limits of quantum theory. Towards this goal we have developed an experimental setup where a macroscopic object,

a mm size dielectric membrane, is cooled close to near absolute zero temperature. We then have observed photon scattering signifying the processes of adding

and subtracting a single motional phonon from the membrane. This achievement paves the road towards generation and detection of highly non-classical states of macroscopic objects.

In a parallel effort we have made progress with the demonstration of a single spin excitation in a macroscopic ensembles of room temperature

atoms.

4). Feasibility studies of application of the negative mass idea to multipartite entanglement involving

spins, photons and massive objects such as mirrors of gravitational wave interferometers.

We have made significant steps towards the development of a "negative-mass quantum noise eater" which can be used for the proof-of-principle demonstration of enhanced sensitivity of

gravitational wave interferometers (GWIs), such as LIGO. We have made progress in development of a critical component of this experiment - a source of entangled light which couples to the atomic negative mass system and to the GWI. A new idea paves the way towards experimentally feasible implementation of the negative mass atomic system.

Progress beyond state of the art achieved so far:

1). Generation of an Einstein-Podolsky-Rosen entangled state of two distant and disparate macroscopic objects, the

mechanical oscillator and the atomic spin oscillator.

2). Generation of two-colour entangled state of light

3). Theoretical basis for enhancement of sensitivity of gravitational wave interferometers using the negative mass atomic noise eater.

4). Demonstration of applications of novel bio-medical applications of atomic quantum magnetometer: magnetocardiography on an isolated animal

heart, detection of low-conductivity objects using eddy current measurements.

Expected results until the end of the project:

Demonstration of quantum teleportation between distant disparate macroscopic objects, an atomic ensemble and a mechanical oscillator.

Demonstration of qubit-type entanglement shared by distant macroscopic objects

Generation of novel non-classical states of matter moving the frontiers of quantum mechanics towards more and more macroscopic objects

Development of a novel atomic platform for quantum state processing based on atoms coupled to two-dimensional dielectric structures.

Novel applications of quantum limited measurements to real life bio-medical problems.

1). Generation of an Einstein-Podolsky-Rosen entangled state of two distant and disparate macroscopic objects, the

mechanical oscillator and the atomic spin oscillator.

2). Generation of two-colour entangled state of light

3). Theoretical basis for enhancement of sensitivity of gravitational wave interferometers using the negative mass atomic noise eater.

4). Demonstration of applications of novel bio-medical applications of atomic quantum magnetometer: magnetocardiography on an isolated animal

heart, detection of low-conductivity objects using eddy current measurements.

Expected results until the end of the project:

Demonstration of quantum teleportation between distant disparate macroscopic objects, an atomic ensemble and a mechanical oscillator.

Demonstration of qubit-type entanglement shared by distant macroscopic objects

Generation of novel non-classical states of matter moving the frontiers of quantum mechanics towards more and more macroscopic objects

Development of a novel atomic platform for quantum state processing based on atoms coupled to two-dimensional dielectric structures.

Novel applications of quantum limited measurements to real life bio-medical problems.