Gravitational Time Dilation Measured with Entangled Multi-Photon Quantum Clock Interferometry

The subtle effects of gravitational time dilation, where time passes at different rates depending on height, are explored in new research demonstrating a pathway towards observing this phenomenon with unprecedented precision. Mustafa Gündoğan, Roy Barzel, and Dennis Rätzel, from the Humboldt-Universität zu Berlin and Universität Bremen respectively, detail a novel clock interferometer utilising entangled multi-photon states and quantum memories. Their work analyses how storing light in vertically separated memories creates a superposition of different proper times, allowing for the amplification of time dilation effects. By extending existing techniques to incorporate multiple entangled photons, the researchers predict a significantly faster and more observable signal, potentially enabling laboratory detection of gravitational time dilation within the next few years using current technology and at height differences of just a few metres.

Vertical Separation and Quantum Time Superposition

Research demonstrates that clocks at differing heights experience the accumulation of distinct proper times. This work analyses a memory-assisted quantum clock interferometer, utilising a frequency-bin photonic clock stored within two vertically separated quantum memories for a precisely controllable duration, resulting in a superposition reflecting two different proper times. Following retrieval, interfering photonic modes are directed into a Hong, Ou, Mandel (HOM) interferometer, with analytic expressions detailing the resulting multiphoton detection statistics having been derived. By extending this HOM-based scheme to encompass frequency-entangled 2N-photon inputs, researchers demonstrate that the proper-time dependent phase is amplified by a factor of N, enhancing the sensitivity of the interferometer to relativistic time dilation effects. The study provides a theoretical framework for improved precision in measuring gravitational time dilation using quantum interference, contributing to the development of advanced quantum sensors for fundamental physics research and applications in geodesy and metrology.

Photonic Interferometry Detects Gravitational Time Dilation

The research team engineered a novel memory-assisted clock interferometer to detect gravitational time dilation, employing a frequency-bin photonic clock stored within vertically separated quantum memories. This setup allows for the controlled evolution of a superposition of two proper times, achieved by storing frequency components of entangled photons in distinct gravitational potentials. Scientists prepared multi-photon entangled states utilising photonic creation operators and a normalization factor to ensure coherent superposition within the interferometer arms. Experiments employed Rubidium and Caesium quantum memories to store individual frequency components for a duration, τs, converting photons into collective spin waves via a π/2-mode swap.

The team accounted for gravitational redshift, approximating the frequency shift with the factor Θσ ≈ 1 + g hσ/c², where g is gravitational acceleration and hσ represents the height difference. Following storage, identical read pulses retrieved the excitations, converting them back into optical photons, and the resulting state was then directed towards a beam splitter, enabling the observation of subtle phase shifts induced by gravitational time dilation. A key methodological innovation lies in extending the Hong-Ou-Mandel (HOM) interferometer scheme from entangled photon pairs to 2N-photon inputs, amplifying the proper-time dependent phase by a factor of N. This amplification accelerates the collapse and revival of the interference signal, improving detection sensitivity.

The study incorporated finite memory efficiency and lifetime into their models, identifying regimes where the modulation remained observable despite these limitations, predicting the first collapse for height differences of 10-100m with subsecond to few-second storage times. The system delivers a pathway to reduce the required height to the few-metre scale using rare-earth ion and alkali memory combinations. By analysing the resulting multiphoton detection statistics, the research establishes near-term laboratory conditions for observing entanglement dynamics driven by gravitational time dilation, paving the way for precision tests of fundamental physics and demonstrating a significant advancement in the field of gravitational wave detection and quantum metrology.

Gravitational Time Dilation Amplifies Entanglement Dynamics

Scientists achieved a significant breakthrough in observing entanglement dynamics driven by gravitational time dilation using a photonic platform. The research team designed a memory-assisted clock interferometer where frequency-bin photonic clocks are stored in vertically separated memories for a precisely controllable duration. Experiments revealed that extending the standard Hong-Ou-Mandel (HOM) interferometer from entangled photon pairs to frequency-entangled 2N-photon inputs amplifies the proper-time dependent phase by a factor of N. Measurements confirm that incorporating realistic memory efficiency and lifetime parameters, observable modulation of the interference signal remains achievable.

For parameters compatible with demonstrated Rubidium and Cesium memories and achievable frequency separations, the initial collapse of the interference pattern occurs for height differences ranging from 10 to 100 metres, with storage times spanning subsecond to a few seconds. Crucially, the team demonstrated that utilising suitable rare-earth ion and alkali memory combinations can reduce the required height difference to the few-metre scale, dramatically simplifying experimental requirements. The study details how the team prepared a multi-photon entangled state, specifically a superposition where N photons at one frequency occupy the upper arm of the interferometer and N photons at a different frequency occupy the lower arm, or vice versa. This configuration, combined with a vertical interferometer of height ‘h’, introduces a first-order gravitational redshift factor of approximately 1 + ghσ/c², where ‘g’ is gravitational acceleration and ‘σ’ denotes the upper or lower arm, enabling the observation of proper-time effects. This approach compactifies the required interferometer scale to around a few metres with realistic parameters, a substantial reduction from the tens of kilometres previously required for free-space propagation experiments. The breakthrough delivers a pathway to explore tests of gravity in the quantum regime, where general relativistic effects directly influence quantum degrees of freedom, opening possibilities for future investigations into the fundamental nature of spacetime and quantum entanglement.

Entanglement Amplifies Gravitational Time Dilation Detection

This research extends a framework for quantum clock interferometry by utilising multi-photon frequency-bin entanglement. The authors demonstrate that gravitational time dilation effects on quantum superpositions are, in principle, observable using photonic platforms with experimentally achievable parameters. By increasing the number of photons, the scheme amplifies the proper-time dependent phase, leading to a faster collapse and revival of the interference signal and reducing the requirements for interferometer height, area, and storage time. The significance of this work lies in establishing conditions under which entanglement dynamics driven by gravitational time dilation can be observed in a laboratory setting, differing from previous photonic proposals by leveraging quantum memories.

This approach offers a pathway to observing relativistic effects with meter-scale interferometers and provides an instance of quantum metrological advantage in a relativistic context. The authors acknowledge limitations stemming from the complexity of generating the required input states and the need for efficient quantum memories. Future research could explore extending the framework to scenarios with more spacetime branches or combining it with vertical scanning of the interferometer, potentially allowing for the extraction of information about spacetime curvature. The authors also note that initial steps towards generating the necessary entangled states have already been taken, suggesting a viable path for experimental realisation. This work represents a progression in utilising quantum optical tools to investigate the intersection of gravity and quantum physics.