Tight bound on finite-resolution quantum thermometry at low temperatures
Precise thermometry is of wide importance in science and technology in general and in quantum systems in particular. Here, we investigate fundamental precision limits for thermometry on cold quantum systems, taking into account constraints due to finite measurement resolution. We derive a tight boun...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2020-09-01
|
| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.033394 |
| _version_ | 1797211284648755200 |
|---|---|
| author | Mathias R. Jørgensen Patrick P. Potts Matteo G. A. Paris Jonatan B. Brask |
| author_facet | Mathias R. Jørgensen Patrick P. Potts Matteo G. A. Paris Jonatan B. Brask |
| author_sort | Mathias R. Jørgensen |
| collection | DOAJ |
| description | Precise thermometry is of wide importance in science and technology in general and in quantum systems in particular. Here, we investigate fundamental precision limits for thermometry on cold quantum systems, taking into account constraints due to finite measurement resolution. We derive a tight bound on the optimal precision scaling with temperature, as the temperature approaches zero. The bound demonstrates that under finite resolution, the variance in any temperature estimate must decrease slower than linearly. This scaling can be saturated by monitoring the nonequilibrium dynamics of a single-qubit probe. We support this finding by numerical simulations of a spin-boson model. In particular, this shows that thermometry with a vanishing absolute error at low temperature is possible with finite resolution, answering an interesting question left open by previous work. Our results are relevant both fundamentally, as they illuminate the ultimate limits to quantum thermometry, and practically, in guiding the development of sensitive thermometric techniques applicable at ultracold temperatures. |
| first_indexed | 2024-04-24T10:24:03Z |
| format | Article |
| id | doaj.art-aa390d084f6541ba80826f3f59583f45 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:24:03Z |
| publishDate | 2020-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-aa390d084f6541ba80826f3f59583f452024-04-12T17:00:23ZengAmerican Physical SocietyPhysical Review Research2643-15642020-09-012303339410.1103/PhysRevResearch.2.033394Tight bound on finite-resolution quantum thermometry at low temperaturesMathias R. JørgensenPatrick P. PottsMatteo G. A. ParisJonatan B. BraskPrecise thermometry is of wide importance in science and technology in general and in quantum systems in particular. Here, we investigate fundamental precision limits for thermometry on cold quantum systems, taking into account constraints due to finite measurement resolution. We derive a tight bound on the optimal precision scaling with temperature, as the temperature approaches zero. The bound demonstrates that under finite resolution, the variance in any temperature estimate must decrease slower than linearly. This scaling can be saturated by monitoring the nonequilibrium dynamics of a single-qubit probe. We support this finding by numerical simulations of a spin-boson model. In particular, this shows that thermometry with a vanishing absolute error at low temperature is possible with finite resolution, answering an interesting question left open by previous work. Our results are relevant both fundamentally, as they illuminate the ultimate limits to quantum thermometry, and practically, in guiding the development of sensitive thermometric techniques applicable at ultracold temperatures.http://doi.org/10.1103/PhysRevResearch.2.033394 |
| spellingShingle | Mathias R. Jørgensen Patrick P. Potts Matteo G. A. Paris Jonatan B. Brask Tight bound on finite-resolution quantum thermometry at low temperatures Physical Review Research |
| title | Tight bound on finite-resolution quantum thermometry at low temperatures |
| title_full | Tight bound on finite-resolution quantum thermometry at low temperatures |
| title_fullStr | Tight bound on finite-resolution quantum thermometry at low temperatures |
| title_full_unstemmed | Tight bound on finite-resolution quantum thermometry at low temperatures |
| title_short | Tight bound on finite-resolution quantum thermometry at low temperatures |
| title_sort | tight bound on finite resolution quantum thermometry at low temperatures |
| url | http://doi.org/10.1103/PhysRevResearch.2.033394 |
| work_keys_str_mv | AT mathiasrjørgensen tightboundonfiniteresolutionquantumthermometryatlowtemperatures AT patrickppotts tightboundonfiniteresolutionquantumthermometryatlowtemperatures AT matteogaparis tightboundonfiniteresolutionquantumthermometryatlowtemperatures AT jonatanbbrask tightboundonfiniteresolutionquantumthermometryatlowtemperatures |